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Supply chain benefits from advanced customer commitments
Journal of Operations Management 18 Ž1999. 61–73 www.elsevier.comrlocaterdsw
Supply chain benefits from advanced customer commitments Stephen M. Gilbert b
a,)
, Ronald H. Ballou
b,1
a College of Business Administration, Management Department, CBA 4.202, The UniÕersity of Texas, Austin, TX 78733, USA Weatherhead School of Management, Case Western ReserÕe UniÕersity, 10900 Euclid AÕenue, CleÕeland, OH 44106-7235, USA
Received 10 January 1998; accepted 6 April 1999
Abstract Buyers are frequently encouraged through price discounts to buy in certain ways — purchase in large quantities or purchase in advance of their needs. Ideally, these pricing incentives can lead to lower costs for both the buyer and the seller. In this paper, a situation is examined where a steel distributor faces stiff competition in its highly undifferentiated service offerings and price is the primary factor in attracting sales. A model is developed that quantifies the benefits to the supplier from obtaining advanced commitments from downstream customers. This model can be used to suggest the maximum price discount that can be offered to customers to encourage them to commit to their orders in advance. Careful balancing of the advanced ordering time with the price discount can lead to cost reductions for both members of the supply channel. q 1999 Elsevier Science B.V. All rights reserved. Keywords: Supply chain coordination; Inventory; Lead time
1. Introduction Historically, attempts to improve upon the operations in a supply chain have focused on reducing the costs associated with individual activities. More recently, attention has been paid to the way in which the activities of one link of the supply chain affect the costs of another, and opportunities are now being recognized that involve coordinating activities across the boundaries of firms in a supply chain. Although the existence of benefits from this sort of coordina-
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Corresponding author. Tel.: q1-512-471-5945 Tel.: q1-216-368-3808; fax: q1-216-368-4776; e-mail: [email protected] 1
tion seem obvious, there is much that needs to be done in terms of identifying and quantifying the specific benefits. The purpose of this paper is to illustrate, based on our experience with a steel distributor, how advanced information about customer needs can be exploited by a make-to-order supplier to reduce operating costs. By offering customers appropriate price reductions in return for providing such information, it is possible to improve the supplier’s profit. The supplier benefits from the customers’ advanced purchase commitments through lower raw material inventory carrying and other operating costs. Customers benefit when these price reductions exceed their costs of committing in advance to their orders. Otherwise, by failing to act on the discounts, the customers are no worse off than they were originally. Thus, these
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S.M. Gilbert, R.H. Ballour Journal of Operations Management 18 (1999) 61–73
price reductions, which are derived from the extent of the advanced commitment and the associated supplier’s cost reduction, serve as a mechanism for improving the overall channel profit. The paper proceeds as follows. After reviewing the relevant literature, we describe the situation observed at a process-to-order steel distributor. We then discuss the dimensions of operational efficiency that might be improved by obtaining advanced commitment from customers in a make-to-order environment, and develop mathematical models for two of these dimensions: raw materials inventory and required production capacity. By applying these models to data from the steel distributor, a graphical representation of the cost effect is developed. This representation serves as a useful tool for determining the maximum price discount that the supplier can afford to offer in return for a given amount of advanced commitment from its customers. 2. Previous research Research on supply chain coordination spans the domains of marketing, economics, and operations management. Jeuland and Shugan Ž1983. identify many of the inherent problems associated with coordinating activities among the members of a supply chain, and describe a variety of mechanisms that can be used to achieve coordination. Improving coordination in a supply chain typically involves one chain member attempting to alter the behavior of at least one other by offering some sort of incentive. If the resulting change in behavior increases the profits of at least one chain member, and does not decrease the profits of any other member, then the total chain is better off. The research associated with supply chain coordination can be divided into two broad classes. The first addresses supply chains that are associated with stable products that have long life cycles, and the second addresses supply chains that are associated with products that have short life cycles and large amounts of demand uncertainty. For supply chains that produce stable, long-lifecycle products, nearly all of the coordination research focuses on how one chain member, i.e., a supplier, can alter the order-quantity ‘‘behavior’’ of its customerŽs. by offering a quantity discount. Sev-
eral papers, including Lal and Staelin Ž1984., Monahan Ž1984., Banerjee Ž1986., and Lee and Rosenblatt Ž1986., consider the role of quantity discounts in an environment in which end demand is unaffected by the size of the discount. Implicitly, this is equivalent to assuming that a downstream channel member does not change price as a result of the discount. Weng Ž1995. departs from this assumption and demonstrates that the optimal all-units quantity discount is equivalent to the optimal incremental quantity discount, but that neither discount form is sufficient to induce the downstream channel member to select the jointly optimal price. At the other end of the spectrum, a few authors have studied the coordination of pricing and ordering decisions in supply chains that produce short-lifecycle products for which demand uncertainty is significant. Paternack Ž1985. and Emmons and Gilbert Ž1998. studied the way in which a manufacturer can offer a returns policy to induce a retailer to make self-interested ordering andror pricing decisions that increase the profits of both parties. Relatively few authors have examined the role that pricing policy can play in obtaining information from downstream supply chain members. Lariviere and Porteus Ž1995. use a Bayesian framework to study the way in which the wholesaler’s pricing schedule affects the retailer’s order quantities, and, hence, the rate at which the retailer learns about the distribution of demand for a new product. To our knowledge, only one paper investigates the way in which price incentives can be used to induce customers to accept longer lead-times for their orders. Moinzadeh and Ingene Ž1993. study a situation in which a distributor sells two partially substitutable products. One of these goods is sold ‘‘from stock’’ for immediate delivery, and the other is sold ‘‘to order’’ for delayed delivery. They demonstrate the conditions under which the profit maximizing strategy involves setting a price for the delayed delivery item that encourages switching to it in order to reduce holding costs for the immediatedelivery item. We are unaware of any research that specifically addresses the benefits that accrue to a supply chain when downstream firms are given incentives to provide earlier commitment to purchases. The purpose of this paper is to develop an approach for identify-
S.M. Gilbert, R.H. Ballour Journal of Operations Management 18 (1999) 61–73
ing and quantifying these benefits to aid a firm in determining the maximum price discount to be offered customers for varying lengths of advanced purchase commitment time. If customers respond to a discount that is less than the maximum one that the supplier can offer, benefits accrue to both channel members. 3. The operating environment at the steel distributor Steel distributors serve three main roles for their customers. First, they provide customers with a means of procuring steel in quantities that are smaller than what steel mills generally service. Second, they provide some value-added processing such as cutting slabs to length, slitting coils, or stamping sheets of steel. Third, they provide transportation. These processing activities add about 25% to the value of the product, since the cost of purchased goods is about 80% of sales. The industry is composed of a large number of firms providing relatively undifferentiated products, and competition is based largely on price. The research presented here is based on the operations at a single facility owned by a relatively large ŽUS$600 million in sales. steel distributor whose operations are believed to be representative of many firms in the industry. Although many of its customers have long term contracts that involve a promise to purchase certain aggregate quantities over some period of time in return for a guaranteed price per ton, there is a large amount of uncertainty about when customers will request specific deliveries. In its current mode of operation, customers provide little or no advanced commitment as to the timing or quantity of their requirements because there is little incentive to do otherwise. For example, even if a customer has ‘‘ordered’’ the delivery of a coil weeks in advance, there is nothing to discourage a cancellation or delay of the order at the last minute. Other customers simply place orders at the last moment. This lack of advanced commitment from customers creates two forms of supply chain inefficiency for this distributor. First, it means that large safety stocks of raw materials must be held. Second, it means that large amounts of excess production capacity must be maintained in order to be able to respond to uncertain demand on very short notice.
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In other environments, advanced customer commitment might also lead to other cost reductions. For example, if production setups were significant, then advanced commitment might allow managers to either combine or re-sequence jobs to reduce the total cost of setups. Alternatively, if production lead times were long, advanced commitment might reduce the need for building-to-forecast instead of building-toorder. ŽSee Raturi et al. Ž1990. for a discussion of build-to-forecast strategies in environments where customer-lead-times are shorter than the production lead-time.. However, neither setups nor production lead-times are significant at the steel distributor with which we interacted, and we have focused our attention on the effect of advanced commitment on safety stock and the amount of excess capacity that is required. To develop greater insight as to how these costs are developed, it is useful to examine the details of the specific firm that we observed. The distributor carries over 200 standard coil types. Although customers provide little or no notice as to their requirements for these coils, the distributor must wait for about 8 weeks for its own orders to be filled by the steel mills. As a result, the distributor must finance huge stocks of raw materials Žinventory turnover is less than 4.0. in order to fill its customer orders. Due to the customized nature of the end product, finished goods inventory is negligible, consisting mainly of coils waiting for the arrival of a truck. In addition to the implications of uncertainty in planning raw material inventories, the firm needs to maintain excess capacity so that it can respond very quickly to the uncertain demand that it receives from its customers. A simplified flow chart of the steps involved in the processing operation at our distributor is shown in Fig. 1. The distributor that we observed has eight machines, each of which performs a slightly different function. These functions include cleaning, slitting, and various forms of stamping, flattening, or chopping. Each machine requires several workers to operate, and in many cases, either skill requirements or union restrictions limit the extent to which workers can be moved from one machine to another. The shop currently operates for a single shift each day plus overtime. In general, overtime must be scheduled in advance. Thus, short-term capacity ad-
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S.M. Gilbert, R.H. Ballour Journal of Operations Management 18 (1999) 61–73
Fig. 1. The supply chain for steel processing.
justments are made primarily through scheduling overtime labor hours. In order to make sure that customer orders can be turned around in less than a day Žmore often than not., the shop schedules more labor hours than the average daily processing requirement. Clearly, the financing of large raw material inventories and the excess production capacity that results from the large amount of uncertainty increases the total supply chain cost. If customers were given an incentive to share information about their requirements with the distributor, there would be opportunities to reduce inventories and to operate at a lower capacity level. By offering customers a discount for committing to their orders in advance, the distributor would encourage buyer behavior that would reduce its own costs. As long as the discount is less than the amount by which its own costs would be reduced, the distributor would be better off. Assuming, of course, that the customers respond to the discount in a rational, self-interested manner, they too might be better off, but would certainly be no worse off. In Section 4, we quantify the amount by which the distributor’s costs would be reduced by various levels of advanced commitment from their customers and then express the cost reduction in the form of a price discount.
4. Model of supply chain costs At the distributor we studied, the demand is created by a relatively large number Ž) 20. of independent customers, each of whom may place more than one independent order per day. The orders placed tend to be small, often requiring only one coil. As a result, the demand can be modeled as a Poisson
process, and the demand during any time interval can be modeled as a Poisson random variable. This model would not be appropriate for situations in which the demand is generated by a few large orders. In the discussion to follow, the terms orders and coils are used inter-changeably, implicitly assuming that each order is for exactly one coil. It is well known that the Poisson distribution can be approximated by a normal distribution when the parameter representing the mean is large. At the steel distributor with which we interacted, the total demand averaged about 60 coilsrday. Thus, the total demand during a time interval of 1 or more days can be approximated by a normal distribution. We denote the mean and standard deviation of the total demand for coils during a period of length L days as Ld tot and 'L s tot , respectively. This demand is composed of requests for n different coil types, and for the most part, these demands are independent of one another. To avoid adding unnecessary complexity, we assume that the distribution of daily demand for each of the n different coil types has mean d s d totrn and standard deviation s s s totr 'n . Note that although the normal approximation may be relatively crude when d s d totrn is very small, it allows us to employ standard inventory models to understand the basic tradeoffs. Under the current mode of operation, customers make almost no advanced commitment to specific shipment timing or quantities. Although some customers do provide preliminary lists of what and when they plan to purchase, there is no incentive to adhere to the expected release dates for these quantities. They frequently change them to better meet their own production requirements. As a result, it is difficult for the distributor to optimize its own operations based on these shifting, uncertain demands.
S.M. Gilbert, R.H. Ballour Journal of Operations Management 18 (1999) 61–73
However, if customers could be convinced to commit to their orders prior to the date upon which they require delivery, then operational exposure to uncertainty could be reduced. Let us suppose that, for some fraction of demand, advanced commitment can be obtained a certain length of time in advance of required delivery. In particular, assume that the fraction b of all demand is ‘‘committed to’’ Lc time units in advance of when delivery is required. Throughout the remainder of the paper, demand for customers providing advanced commitment will be referred to as committed demand, and demand for which no such advanced commitment is provided will be referred to as regular demand. In the following sections, we develop models for quantifying the amount by which the costs of raw material inventory and excess capacity are reduced when a fraction b of demand is committed Lc time units in advance. 4.1. The effect of prior ordering commitments upon raw material inÕentory costs Given the above characterization of the demands for each coil type, we can develop a model of the effects of advanced commitments from customers upon raw material inventory costs by making an appropriate modification to a traditional continuous review re-order point inventory model. ŽAt the steel distributor, purchasing is based on a continuous review re-order point policy.. As described below, the modification involves the determination of the standard deviation of lead time demand as a function of the proportion of committed customers and the length of their commitment. Let S be the ordering cost that is incurred each time the distributor places an order for one of the n coil types Žitems.. Let h be the cost of holding one unit of inventory for 1 day, and assume that it is the same for all coil types. At the distributor with which we interacted, customers tend to have more than one source of supply. If one supplier is out of stock on a particular item, they can generally obtain it elsewhere. Therefore, it is assumed that if demand for a given item occurs while the distributor is out of stock on that item, then the demand is lost. Let k be the cost of each unit of lost demand. The lead time from the steel mills Žthe supplier to the distributor. is
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Ls . For purposes of illustration, we assume that the length of supply lead time Ž Ls . is deterministic. In order to determine the optimal continuous review Ž s,S . inventory policy, the demand distribution that is appropriate for each of the n items during the lead time must first be characterized. To do this, the regular demand will be analyzed separately from committed demand. The daily demand of regular customers for each of the n items is approximately normally distributed with mean d r s Ž1 y b . d and standard deviation sr s s Ž 1 y b . . Therefore, using standard probability theory results, the regular demand during the lead time is normally distributed with mean and standard deviation:
(
d L r s Ž 1 y b . dLs
(
(
sL r s sr 2 Ls s s 2 Ls Ž 1 y b . s s Ls Ž 1 y b . .
(
Ž 1. The daily committed demand has mean d c s b d and a standard deviation sc s s b . However, for the committed demand, the distributor is not exposed to demand uncertainty over the entire length of the raw material supply lead-time from the mill. As depicted in Fig. 2, at the time that the distributor orders raw material from the steel mill, it has already received all information about committed demand that will need to be satisfied within the next L c time units. Therefore, it knows with certainty how many coils it will have to ship to satisfy committed demand during the next L c time units. This is the benefit of advanced commitment. However, at the time it orders raw material from the mill, the distributor has not yet been informed as to the amount of committed demand that will need to be satisfied during the last Ls y Lc units of time during the raw material lead time from the mill. Therefore, as shown in Fig. 2, the distributor is exposed to the uncertainty of committed demand during the interval labeled as Ls y Lc .
'
Fig. 2. The distributor’s exposure to demand uncertainty from ‘‘committed’’ customers during an order cycle.
S.M. Gilbert, R.H. Ballour Journal of Operations Management 18 (1999) 61–73
66
To formalize this, let t be a point in time at which an order is to be placed with the steel mill, and let x t be the number of outstanding committed orders at time t. In other words, at time t, it is known that exactly x t coils must be shipped to satisfy committed demand during the next Lc time units. In addition to this known demand, there is also the unknown portion of committed demand that will have to be satisfied during the lead time. This unknown portion of committed demand consists of the requests that are received from customers after the raw material is ordered from the mill, but that also need to be satisfied before the raw material is received from the mill. It is normally distributed with mean d c Ž Ls y L c . and standard deviation sc Ls y Lc . Recall that d c s b d and sc s s b . Therefore, by substituting for d r and sr , the total committed demand that needs to be satisfied during the supply lead time is normally distributed with the following mean and standard deviation:
(
'
d L c s x t q b d Ž Ls y L c .
(
sL c s s b Ž Ls y L c .
where Q is the order quantity, and EŽ z . is the unit normal loss function. Setting the derivatives of C with respect to Q and z to zero yields: QU s
(
2 d Ž S q k sL E Ž z . . h
PU s
kd Qh q kd
Ž 5.
where P U is the optimal probability with which there is a stockout in a given replenishment cycle. Note that for a given value of P U , the corresponding value of z can be found in a table of the cumulative standard normal distribution. Therefore, an iterative procedure can be used to solve for QU and P U . By substituting these optimal values back into Eq. Ž4., the optimal cost of ordering and stocking the raw material for each of the n items for any combination of Lc and b can be calculated. Note that the above model is not specific to the steel distributor that we observed. Indeed, it can be applied to any item that is managed by a continuous review inventory policy and for which the demand can reasonably be modeled as a Poisson process.
Ž 2. The regular and committed demand can now be combined to see that the total demand during the lead time is normally distributed with the following mean and standard deviation: d L s x t q b d Ž Ls y Lc . q Ž 1 y b . dLs s x t q d Ž Ls y b L c .
Ž 3a .
( s s(L y b L
Ž 3b .
sL s s b Ž Ls y L c . q Ls Ž 1 y b . s
c
A traditional approximate cost model for lost sales can now be developed to analyze the total cost per day for procuring and stocking raw materials for each of the n items. Average cost per day s ordering cost q shortage cost q holding cost Ž regular andsafety stock . Cs
d Q
Sqh
ž
Q 2
/
q sL E Ž yz . q
d Q
k sL E Ž z . Ž 4 .
4.2. The effect of prior ordering commitments upon the cost of excess capacity The uncertainty about customer requirements may also make it necessary to maintain large amounts of excess capacity in production equipment, labor force, and storage space. However, if some customers provided advanced commitment, it would be possible to smooth the rate of production. Hence, less total production capacity would be needed to satisfy customers’ needs in a timely fashion. Consider the following situation for 2 consecutive days: Suppose that on the first day there is less demand than can be met with the scheduled capacity, and that on the second day there is more demand than can be met with the scheduled capacity. In the current mode of operations, workers will be idle for part of the day on the first day, and orders would either be late or go unfilled on the second day. Alternatively, if some of the customers for the second day had given advanced commitment, their orders could have been processed on the first day, freeing up capacity for other customers later on.
S.M. Gilbert, R.H. Ballour Journal of Operations Management 18 (1999) 61–73
The above example demonstrates how advanced commitment from customers allows a make-to-order firm to smooth its production rate. To approximate the way that advanced customer commitments affect the amount of excess capacity that is needed, we use a simple queuing model. Let us denote the expected amount of time between the receipt of a customer order and the completion of its processing by W. We assume that in order to insure that due date commitments can be filled, management maintains enough capacity so that, the average time ŽW . within which an order can be filled is no larger than some fraction Žwhich we denote by c . of the quoted lead time. For example, if customers are being quoted a lead time of L time units, then we assume that processing capacity must be sufficiently large that the expected time to complete an order is W s c L. For simplicity, we assume that processing times are exponentially distributed and that the arrival of orders is a Poisson process. This allows us to analyze the workload on each machine as an MrMr1 queue. Although actual processing times are not exponentially distributed, this approach allows us to develop a simple model that provides insight as to the general tradeoff between advanced commitment and the amount of excess capacity that must be maintained. Recall, from standard results for an MrMr1 queue, that for a given rate of demand Ž l. and processing capacity Ž m ., the expected time to complete an order ŽW . can be expressed as follows: Ws
myl
W s b Wc q Ž 1 y b . Wr
1
c Lr
Ž 8.
To make sure that the expected turn-around time for regular customers is no larger than Wr F c L r , recall that under the assumed queue discipline, orders from committed customers are never allowed to interfere with the processing of regular customers orders. Therefore, expected turn-around time for regular customers depends only on the arrival rate of regular customers, and is independent of the arrival rate of committed customers. Therefore, for any given amount of capacity Ž m ., we have: y1
Ž 9.
Ž 6. Thus, in order to make sure that we have adequate capacity to satisfy regular customers, we need:
Thus, given Lr , l, and c , we can easily compute the amount of capacity that is required if all orders must be filled within the same Žregular. lead time.
mGlq
advantage of this flexibility would be to assign these orders lower processing priority. Therefore, let us assume that two queues are maintained: one for committed customers and one for regular customers. Within each queue, orders are processed first-comefirst-served, but regular customers are always given priority over committed customers. Let us denote the required expected turn-around time for regular and committed customers by Wr and Wc , respectively. Note that because the distribution of processing time does not depend on the type of customer, this processing scheme will not change the overall average expected time ŽW . to complete an order for a given level of capacity Ž m .. It will simply allow the regular customers’ orders to be finished faster at the expense of committed customers. Thus, for a given level of capacity m :
Wr s Ž m y Ž 1 y b . l .
1
67
Ž 7.
Now suppose that some fraction b of orders can be completed in a longer lead-time of Lc . To analyze how this affects the amount of capacity that is required, note that the longer lead time for committed customers affords a certain amount of flexibility in the processing of these orders. One way to take
mG Ž1yb . lq
1
Ž 10 .
c Lr
At the same time, we need to make sure that we have enough capacity to provide an expected turnaround time for committed customers of no more than c Lc . By substituting Eqs. Ž6. and Ž9. into Eq. Ž8. and solving for Wc , we have that, for a given amount of capacity Ž m .: Wc s
1
ž
1yb
1
b myl
y
my Ž1yb . l
/
Ž 11 .
S.M. Gilbert, R.H. Ballour Journal of Operations Management 18 (1999) 61–73
68
Thus, in order to make sure that we have adequate capacity to satisfy committed customers, we need to have adequate capacity to insure that Wc F c Lc . Substituting this inequality into Eq. Ž11. and performing some algebraic manipulations, we get:
mG
1 2 c Lc
ž Ž 2 y b . lc L q1
(
c
2
q Ž lc Lc b q 1 . q 4lc Lc Ž 1 y b .
/
Ž 12 .
We need to make sure that we have sufficient capacity to satisfy constraints Ž11. and Ž12., in order to satisfy our regular and committed customers, respectively. The total amount of capacity that we need for any combination of l, L r , Lc , c , and bc is the maximum of the right hand sides to these two inequalities. Note that this model is a somewhat abstract representation of the actual capacity requirement. This is due to its assumptions of exponentially distributed processing times, its emphasis on expected turnaround times, and the fact that it assumes that regular customers are given absolute priority over committed customers. However, in spite of these limitations, the model does represent the general effect that increased processing flexibility from committed customers can have on the amount of capacity that is required.
5. Typical results In order to illustrate how our model can be used, we draw upon data that is representative of the steel distributor that motivated this work. In particular, there are about 250 different types of coils that must be processed. We estimated the mean and standard deviation of daily demand to be about d tot s 60 and s tot s 7.8, respectively. ŽNote that this implies a coefficient of variation that is consistent with a Poisson process.. For simplicity, we assumed that this demand is spread uniformly across the 250 coil types, so that the daily demand for each coil type has mean d s 0.24 and s s 0.5. Based on the potential for lost profits, stockout costs Ž k . were estimated to be US$243rcoil. Holding costs were estimated based on the opportunity cost of capital. Since the average
cost of a coil is about US$2000, and the annual cost of capital is approximately 25%, we took h s US$2 per unit per day. On average, raw material lead time from the mills is about 8 weeks, so we assume Ls s 40 days. To estimate the order processing cost, we observed that each time an order is placed, long-distance telephone calls are made to suppliers to check stock availability, delivery times, and prices, hourly clerical personnel need to be compensated for the time that they spend, and a shipping charge is incurred based on the order size. Based on these events, we estimated Žconservatively. the order processing cost to be S s US$50rorder. Each of the eight machines in the shop can process about eight coils in an 8-h shift. Although between one and three workers are typically needed to operate a machine, we assume that exactly two workers are needed for each of the machines. Recall that each machine performs a slightly different function, therefore, each customer order must be processed on a specific machine. For simplicity, we assume that the average rate of demand is the same for all eight machines. In particular, we assume that the demand processed on each machine is a Poisson process with rate l s d totr8 s 7.5 coilsrday. Currently, the shop schedules about 1.5 h of overtime per day at each machine. Based on the model presented in Eq. Ž7. this implies that c s 0.5. The operators are paid US$18rh for regular shift, and US$24rh for overtime, including benefits. Since union rules preclude scheduling less than a normal 8-h shift, we define excess capacity as the amount of overtime labor that needs to be scheduled. Each machine requires an average of two operators. Therefore, the cost of excess capacity on each machine is US$48rh. With this information, our model can be used to estimate the supply chain costs for various fractions of committed customers Ž b . and the number of days in advance that committed customers give for their orders Ž Lc .. The results of our model are shown in the graphs of Fig. 3. Fig. 3a and b show separately how the annual costs associated with raw materials and excess capacity are affected. As should be expected, both costs decrease in the fraction of demand that is committed in advance. What is perhaps more interesting is the way in which the costs decrease. Since raw material costs tend to be concave in b , the
S.M. Gilbert, R.H. Ballour Journal of Operations Management 18 (1999) 61–73
69
vance notice Ž b s 0., the combined cost of holding raw materials inventory and excess capacity is US$1,179,000 per year. On the other hand, if 50% of the customers commit to firm orders just 6 days in advance of processing Ž Lc s 6., the company can realize an annual cost reduction of US$1,179,000 y 1,026,214 s US$152,786. As can be seen from the graph, the higher the fraction of demand that is committed and the longer the length of time commitment, the greater the potential cost reduction is for the steel distributor. Obviously, the maximum cost reduction is achieved when all orders are placed at least 40 days in advance of processing. Commitments longer than the replenishment lead time from the steel mills offer no further advantage to the steel distributor. The value of the chart in Fig. 3c is that it provides a tool for aligning pricing policy with operating costs. By communicating the cost implications of various levels of commitment from customers to sales representatives, it becomes possible to develop pricing policies that are more consistent with operating costs.
6. Generating a pricing policy
Fig. 3. Ža. Annual raw material inventory costs as a function of the fraction of the customers committing to firm orders Ž b . and the time in advance of processing Ž Lc . in days. Žb. Annual cost of excess capacity Žovertime. as a function of the fraction of the customers committing to firm orders Ž b . and the time in advance of processing Ž Lc . in days. Žc. Combined annual cost of inventory and excess capacity as a function of the fraction of the customers committing to firm orders Ž b . and the time in advance of processing Ž Lc . in days.
incremental cost reductions become larger as more demand is committed. In contrast, since the costs of production schedule changes tend to be convex in b , the incremental cost reductions become smaller as more demand is committed. Fig. 3c shows the magnitude of the combined annual cost reductions for this particular configuration of costs, demand, and lead times. In the current mode of operation where no customers provide ad-
Customers currently provide little advanced information about their requirements. Even though customers may know far in advance that they will need a certain number of coils of a particular coil type on a specific date, there is currently no incentive for them to provide this information to the steel distributor. These same customers apply nearly constant pressure on the distributor to reduce prices, resulting from their own cost reduction programs and the competitive nature of the undifferentiated service that the distributor provides. Unfortunately, the steel distributor has limited ability to reduce the prices without reducing operating expenses, as prices already reflect the current state of order uncertainty. As discussed in Section 5, one way for the steel distributor to reduce its costs is by obtaining advanced commitment from customers. Although this sort of advanced commitment reduces the customers’ flexibility, not all customers require the same amount of flexibility to change their orders. A single customer may not even require the same amount of
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S.M. Gilbert, R.H. Ballour Journal of Operations Management 18 (1999) 61–73
flexibility for every coil ordered. For example, suppose that a customer has planned a production batch that requires two to four steel coils, the exact quantity to be determined on the production date. Since this customer will certainly need at least two coils, an order is submitted for two coils, while allowing flexibility to order the other one or two at a later time. Note that under the current policy, all customers pay for infinite flexibility for every coil. Therefore, many customers will likely provide advanced commitment to at least some of their orders in return for a lower price per coil. This seems reasonable since customers seek lower prices on a highly substitutable service as long as the price reduction exceeds the disadvantage of less ordering flexibility. 6.1. A conceptual approach to pricing policy In order to develop a pricing policy, we would need to estimate the responsiveness of customers to various levels of discounts and lengths of commitment. To illustrate, suppose that a discount will be offered for a single level of commitment. Let p be the percent discount that is applied to each coil to which a customer provides advanced commitment. The fraction of demand that is committed in response to a given discount depends upon both the magnitude of the discount and the length of commitment. Thus, we can represent this fraction as a function b Ž p, Lc . which can reasonably be assumed is increasing in p and decreasing in Lc . Although the sales staff may have some intuition about the general shape of this function, it is likely that some experimentation would be necessary in order to quantify it. When a discount is offered, both the distributor’s revenue and costs will be affected. Let RŽ p, Lc . be the distributor’s revenue when a discount of p percent is offered to customers agreeing to provide commitment to their orders L c time units in advance. Denoting the distributor’s current revenue by R, this function can be expressed as: R Ž p, Lc . s Ž 1 y pb Ž p, Lc . . R
Ž 13 .
Note that this revenue function implies that the only effect of the discount upon demand is to encourage
customers to make advanced order commitment, where the total magnitude of demand is unaffected by the discount. This is consistent with Lal and Staelin Ž1984., Monahan Ž1984., Banerjee Ž1986. and Lee and Rosenblatt Ž1986., and is reasonable when the output levels of downstream customers are relatively insensitive to their costs associated with this particular input. To the extent that this assumption is not valid, we would need to include a stimulation effect in Eq. Ž13.. Fig. 3c depicts the distributor’s costs as a function of committed customers. Denote this relationship as C Ž b , Lc .. Once the function b Ž p, Lc . has been estimated, the distributor’s costs can be expressed as C Ž bc Ž p, L c ., L c .. From Fig. 3c, it can be observed that C Ž. is decreasing in both of its arguments. For a given length of commitment, b Ž p, L c . is increasing in p. It follows that C Ž b Ž p, Lc ., Lc . is decreasing in p. The distributor’s profit can be expressed as the following function: Profit Ž p, L c . s R Ž p, Lc . y C Ž b Ž p, Lc . , Lc . Ž 14 . The optimal pricing policy can be identified by optimizing first with respect to p, and then with respect to L c . In general, maximizing Eq. Ž14. with respect to p for a given L c is not easy because it is not necessarily concave, or even unimodal. However, in many industrial markets, there are classes of customers that face similar cost tradeoffs and might be expected to respond similarly to one another. In such a case, for a given value of L c the function b Ž p, Lc . will resemble a step function, greatly simplifying the process of identifying the optimal discount pU Ž L c . for a given lead time. Assuming that only one combination of discount and length of commitment is to be offered, then need is only to compare ProfitŽ pU Ž L c ., Lc . across the range of Lc . 6.2. A pragmatic approach to deÕeloping a pricing policy In order to develop a pricing policy that is mutually beneficial to both the distributor and the downstream customers, the results shown in Fig. 3c can be drawn upon. From our example, regular customers are currently charged a price of US$2500rcoil. Given that the average daily demand is 60 and there are
S.M. Gilbert, R.H. Ballour Journal of Operations Management 18 (1999) 61–73
250 working days per year, the average annual demand is 15,000 coils. Suppose that a price reduction is offered on each coil for which customers give 40 days advanced notice. If a target number of 50% of coils will be ordered with advanced commitment, the maximum cost reduction to be realized by the steel distributor is US$1,179,000 y 869,000 s US$310,000 per year. Since 50% of the 15,000 coils are expected to be affected by the cost reduction, the savings per coil is US$310,000r7500 s US$41.33. This is approximately 8% of the value added by the steel distributor Ž20% = US$2500.. This is the maximum price reduction that can be offered to entice 50% of the customers to commit to their orders 40 days in advance. If these customers can be enticed with a smaller price reduction, then the distributor will be better off. Since the company does not now price in this fashion, it is not known how customers will respond to the price incentive. That is, the fraction of orders that will be committed is not known for a particular price reduction amount. However, experimenting with different price reductions for various commitment times will give the likely fraction of committed orders to result from a given price discount level. The price incentive can be refined so that b , Lc , and the price reduction are in conformance. The economics expressed in Fig. 3c provide the basis for determining the effective price discount. That is,
71
when the price sensitivity of the customer is generally understood, Fig. 3c can be reviewed to see if the price reduction being offered does not exceed the maximum allowed. Ideally, there exists a discount less than the distributor’s maximum for which an appropriate portion of buyers would benefit from commitment. If so, both the committed customers and the distributor are better off. On the other hand, because customers can reject the discount and continue buying as they always have, none of them will be any worse off after the discount is offered. Example. Table 1 represents the maximum percent price discount that can be offered to induce various amounts of commitment as measured by b and L c . Lower price discounts may actually be offered so that the distributor benefits as well. For a given combination of b and Lc , the table represents the average savings in raw materials and excess capacity costs per committed coil expressed as a fraction of price. Using our previous notation, it is generated by taking C Ž b , Lc . y C Ž0,0., which can be obtained from Fig. 3, and dividing this cost savings by the number of committed customers. This per-coil saving is then divided by the coil list price. Once the customer response to price is approximately known, the body of the table can be searched for a price discount schedule that offers different price discount levels for various advanced commitment times. To obtain 12 days of commitment from 60% of the orders, the distributor can offer a dis-
Table 1 Maximum percent price discount that can be offered for various advanced customer order commitment times Fraction of committed customers, b
Advanced commitment Ž Lc . in days 0 6 12
24
32
40
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
2.32 2.38 1.76 1.44 1.26 1.14 1.06 1.00 0.96 0.94
2.50 2.54 1.92 1.62 1.42 1.34 1.28 1.24 1.24 1.24
2.68 2.70 2.10 1.80 1.66 1.58 a 1.54 1.56 1.62 1.98
a
1.64 1.24 1.04 0.92 0.82 0.74 0.66 0.60 0.54 0.50
2.10 1.96 1.50 1.20 1.00 0.88 0.78 0.72 0.66 0.64
Example calculation: From Fig. 3c, the cost for b s 0.6 and L c s 0 is US$1,179,000 and for b s 0.6 and Lc s 40 is US$825,000. Total savings is US$1,179,000 y 825,000 s US$354,000. Coils affected are b = 15,000 or 9000. Savings per coil is US$354,000rŽ0.6 = 15,000. s US$39.33. Percent price reduction is Ž39.33rUS$2500. = 100 s 1.58%.
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S.M. Gilbert, R.H. Ballour Journal of Operations Management 18 (1999) 61–73
count of up to 0.88%. On the other hand, to obtain 40 days of commitment from 60% of the orders, the distributor can offer a discount of up to 1.58%. If more customers wish to take advantage of the price discount than the fraction b associated with a particular price, it may be necessary to limit the availability of the discount or to adjust the amount of the discount until it is balanced with b . Although the percentage discounts in this example appear to be small, they are not necessarily insignificant, particularly for customers in highly competitive industries where a large portion of the cost of goods sold is represented by steel purchases. For example, consider a customer for whom profit margins are 10% and steel costs represent 80% of sales. Even a discount of 1.0% off of all its purchases represents an 8% increase in profits. Moreover, if the discount offered is not large enough for a particular customer to change its order commitment patterns, the customer simply stays with the current, flexible order pattern. Although neither party realizes any benefit from this action, neither one is worse off when customers continue their current ordering-pricing practices. The example illustrates how the results of this research might be used.
7. Conclusions In this paper, a situation has been described in which the failure to obtain reliable advanced notice about customer requirements has resulted in some cost inefficiencies for a steel distributor. For this particular firm, the inefficiencies involved raw material inventories and excess production capacity. Although the specific sources of inefficiency may differ from one firm or industry to another, there are many opportunities to eliminate inefficiency in the supply chain by creating incentives for downstream members to provide advanced notice to their upstream partners about their needs. A general concept has been provided and some price discount bounds for a supplier to use advanced order commitments as a means of offering lower prices. There is little research to indicate that advanced order commitments has been studied as a basis for price discounting. We hope that this work provides some initial insights that will lead to further research in this area.
Like many firms, the steel distributor that was studied followed an industry norm Žthat of allowing customers infinite flexibility to place or change their orders. without carefully considering the implications of this practice. Since this practice drives up the marginal costs in the industry, it creates an opportunity for a firm to offer slightly less flexibility to customers in the form of early order commitment, in exchange for lower prices. However, it is only by understanding the cost implications of advanced ordering that a firm can offer price incentives benefiting both itself and its customers. The model presented provides a useful tool for estimating the cost savings associated with various levels of advanced order commitment. Although the focus on the costs of raw materials and excess capacity is specific to the steel distributor that motivated this research, the general approach can be applied to a wide variety of firms. Even though the specific nature of cost implications may differ from industry to industry, there are many opportunities for firms to offer their customers price reductions in return for early order commitment. It has been demonstrated that industrial firms can quantify the cost reductions associated with early commitments from customers, paving the way for new pricing policies that benefit both themselves and their customers.
References Banerjee, A., 1986. A joint economic-lot-size model for purchaser and vendor. Decision Sciences 17 Ž3., 292–310. Emmons, H., Gilbert, S., 1998. The role of returns policies in pricing and inventory decisions for catalogue goods. Management Science 44 Ž2., 276–283. Jeuland, A., Shugan, S., 1983. Managing channel profits. Marketing Science 2 Ž3., 239–272. Lal, R., Staelin, R., 1984. An approach for developing an optimal discount pricing policy. Management Science 30 Ž12., 1524– 1539. Lariviere, M., Porteus, E., 1995. Informational dynamics and new product pricing. Stanford University Working Paper. Lee, H., Rosenblatt, M., 1986. A generalized quantity discount pricing model to increase supplier’s profits. Management Science 33 Ž9., 1167–1185. Moinzadeh, K., Ingene, C., 1993. An inventory model of immedi-
S.M. Gilbert, R.H. Ballour Journal of Operations Management 18 (1999) 61–73 ate and delayed delivery. Management Science 39 Ž5., 536– 548. Monahan, J.P., 1984. A quantity discount pricing model to increase vendor profits. Management Science 30 Ž6., 720–726. Paternack, B.A., 1985. Optimal pricing and return policies for perishable commodities. Marketing Science 4 Ž2., 166–176.
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Raturi, A.S., Meredith, J.R., McCutcheon, D.M., Camm, J.D., 1990. Coping with the build-to-forecast environment. Journal of Operations Management 9 Ž2., 230–249. Weng, Z.K., 1995. Channel coordination and quantity discounts. Management Science 41 Ž9., 1509–1522.
Supply chain benefits from advanced customer commitments Stephen M. Gilbert b
a,)
, Ronald H. Ballou
b,1
a College of Business Administration, Management Department, CBA 4.202, The UniÕersity of Texas, Austin, TX 78733, USA Weatherhead School of Management, Case Western ReserÕe UniÕersity, 10900 Euclid AÕenue, CleÕeland, OH 44106-7235, USA
Received 10 January 1998; accepted 6 April 1999
Abstract Buyers are frequently encouraged through price discounts to buy in certain ways — purchase in large quantities or purchase in advance of their needs. Ideally, these pricing incentives can lead to lower costs for both the buyer and the seller. In this paper, a situation is examined where a steel distributor faces stiff competition in its highly undifferentiated service offerings and price is the primary factor in attracting sales. A model is developed that quantifies the benefits to the supplier from obtaining advanced commitments from downstream customers. This model can be used to suggest the maximum price discount that can be offered to customers to encourage them to commit to their orders in advance. Careful balancing of the advanced ordering time with the price discount can lead to cost reductions for both members of the supply channel. q 1999 Elsevier Science B.V. All rights reserved. Keywords: Supply chain coordination; Inventory; Lead time
1. Introduction Historically, attempts to improve upon the operations in a supply chain have focused on reducing the costs associated with individual activities. More recently, attention has been paid to the way in which the activities of one link of the supply chain affect the costs of another, and opportunities are now being recognized that involve coordinating activities across the boundaries of firms in a supply chain. Although the existence of benefits from this sort of coordina-
)
Corresponding author. Tel.: q1-512-471-5945 Tel.: q1-216-368-3808; fax: q1-216-368-4776; e-mail: [email protected] 1
tion seem obvious, there is much that needs to be done in terms of identifying and quantifying the specific benefits. The purpose of this paper is to illustrate, based on our experience with a steel distributor, how advanced information about customer needs can be exploited by a make-to-order supplier to reduce operating costs. By offering customers appropriate price reductions in return for providing such information, it is possible to improve the supplier’s profit. The supplier benefits from the customers’ advanced purchase commitments through lower raw material inventory carrying and other operating costs. Customers benefit when these price reductions exceed their costs of committing in advance to their orders. Otherwise, by failing to act on the discounts, the customers are no worse off than they were originally. Thus, these
0272-6963r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 2 7 2 - 6 9 6 3 Ž 9 9 . 0 0 0 1 2 - 1
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S.M. Gilbert, R.H. Ballour Journal of Operations Management 18 (1999) 61–73
price reductions, which are derived from the extent of the advanced commitment and the associated supplier’s cost reduction, serve as a mechanism for improving the overall channel profit. The paper proceeds as follows. After reviewing the relevant literature, we describe the situation observed at a process-to-order steel distributor. We then discuss the dimensions of operational efficiency that might be improved by obtaining advanced commitment from customers in a make-to-order environment, and develop mathematical models for two of these dimensions: raw materials inventory and required production capacity. By applying these models to data from the steel distributor, a graphical representation of the cost effect is developed. This representation serves as a useful tool for determining the maximum price discount that the supplier can afford to offer in return for a given amount of advanced commitment from its customers. 2. Previous research Research on supply chain coordination spans the domains of marketing, economics, and operations management. Jeuland and Shugan Ž1983. identify many of the inherent problems associated with coordinating activities among the members of a supply chain, and describe a variety of mechanisms that can be used to achieve coordination. Improving coordination in a supply chain typically involves one chain member attempting to alter the behavior of at least one other by offering some sort of incentive. If the resulting change in behavior increases the profits of at least one chain member, and does not decrease the profits of any other member, then the total chain is better off. The research associated with supply chain coordination can be divided into two broad classes. The first addresses supply chains that are associated with stable products that have long life cycles, and the second addresses supply chains that are associated with products that have short life cycles and large amounts of demand uncertainty. For supply chains that produce stable, long-lifecycle products, nearly all of the coordination research focuses on how one chain member, i.e., a supplier, can alter the order-quantity ‘‘behavior’’ of its customerŽs. by offering a quantity discount. Sev-
eral papers, including Lal and Staelin Ž1984., Monahan Ž1984., Banerjee Ž1986., and Lee and Rosenblatt Ž1986., consider the role of quantity discounts in an environment in which end demand is unaffected by the size of the discount. Implicitly, this is equivalent to assuming that a downstream channel member does not change price as a result of the discount. Weng Ž1995. departs from this assumption and demonstrates that the optimal all-units quantity discount is equivalent to the optimal incremental quantity discount, but that neither discount form is sufficient to induce the downstream channel member to select the jointly optimal price. At the other end of the spectrum, a few authors have studied the coordination of pricing and ordering decisions in supply chains that produce short-lifecycle products for which demand uncertainty is significant. Paternack Ž1985. and Emmons and Gilbert Ž1998. studied the way in which a manufacturer can offer a returns policy to induce a retailer to make self-interested ordering andror pricing decisions that increase the profits of both parties. Relatively few authors have examined the role that pricing policy can play in obtaining information from downstream supply chain members. Lariviere and Porteus Ž1995. use a Bayesian framework to study the way in which the wholesaler’s pricing schedule affects the retailer’s order quantities, and, hence, the rate at which the retailer learns about the distribution of demand for a new product. To our knowledge, only one paper investigates the way in which price incentives can be used to induce customers to accept longer lead-times for their orders. Moinzadeh and Ingene Ž1993. study a situation in which a distributor sells two partially substitutable products. One of these goods is sold ‘‘from stock’’ for immediate delivery, and the other is sold ‘‘to order’’ for delayed delivery. They demonstrate the conditions under which the profit maximizing strategy involves setting a price for the delayed delivery item that encourages switching to it in order to reduce holding costs for the immediatedelivery item. We are unaware of any research that specifically addresses the benefits that accrue to a supply chain when downstream firms are given incentives to provide earlier commitment to purchases. The purpose of this paper is to develop an approach for identify-
S.M. Gilbert, R.H. Ballour Journal of Operations Management 18 (1999) 61–73
ing and quantifying these benefits to aid a firm in determining the maximum price discount to be offered customers for varying lengths of advanced purchase commitment time. If customers respond to a discount that is less than the maximum one that the supplier can offer, benefits accrue to both channel members. 3. The operating environment at the steel distributor Steel distributors serve three main roles for their customers. First, they provide customers with a means of procuring steel in quantities that are smaller than what steel mills generally service. Second, they provide some value-added processing such as cutting slabs to length, slitting coils, or stamping sheets of steel. Third, they provide transportation. These processing activities add about 25% to the value of the product, since the cost of purchased goods is about 80% of sales. The industry is composed of a large number of firms providing relatively undifferentiated products, and competition is based largely on price. The research presented here is based on the operations at a single facility owned by a relatively large ŽUS$600 million in sales. steel distributor whose operations are believed to be representative of many firms in the industry. Although many of its customers have long term contracts that involve a promise to purchase certain aggregate quantities over some period of time in return for a guaranteed price per ton, there is a large amount of uncertainty about when customers will request specific deliveries. In its current mode of operation, customers provide little or no advanced commitment as to the timing or quantity of their requirements because there is little incentive to do otherwise. For example, even if a customer has ‘‘ordered’’ the delivery of a coil weeks in advance, there is nothing to discourage a cancellation or delay of the order at the last minute. Other customers simply place orders at the last moment. This lack of advanced commitment from customers creates two forms of supply chain inefficiency for this distributor. First, it means that large safety stocks of raw materials must be held. Second, it means that large amounts of excess production capacity must be maintained in order to be able to respond to uncertain demand on very short notice.
63
In other environments, advanced customer commitment might also lead to other cost reductions. For example, if production setups were significant, then advanced commitment might allow managers to either combine or re-sequence jobs to reduce the total cost of setups. Alternatively, if production lead times were long, advanced commitment might reduce the need for building-to-forecast instead of building-toorder. ŽSee Raturi et al. Ž1990. for a discussion of build-to-forecast strategies in environments where customer-lead-times are shorter than the production lead-time.. However, neither setups nor production lead-times are significant at the steel distributor with which we interacted, and we have focused our attention on the effect of advanced commitment on safety stock and the amount of excess capacity that is required. To develop greater insight as to how these costs are developed, it is useful to examine the details of the specific firm that we observed. The distributor carries over 200 standard coil types. Although customers provide little or no notice as to their requirements for these coils, the distributor must wait for about 8 weeks for its own orders to be filled by the steel mills. As a result, the distributor must finance huge stocks of raw materials Žinventory turnover is less than 4.0. in order to fill its customer orders. Due to the customized nature of the end product, finished goods inventory is negligible, consisting mainly of coils waiting for the arrival of a truck. In addition to the implications of uncertainty in planning raw material inventories, the firm needs to maintain excess capacity so that it can respond very quickly to the uncertain demand that it receives from its customers. A simplified flow chart of the steps involved in the processing operation at our distributor is shown in Fig. 1. The distributor that we observed has eight machines, each of which performs a slightly different function. These functions include cleaning, slitting, and various forms of stamping, flattening, or chopping. Each machine requires several workers to operate, and in many cases, either skill requirements or union restrictions limit the extent to which workers can be moved from one machine to another. The shop currently operates for a single shift each day plus overtime. In general, overtime must be scheduled in advance. Thus, short-term capacity ad-
64
S.M. Gilbert, R.H. Ballour Journal of Operations Management 18 (1999) 61–73
Fig. 1. The supply chain for steel processing.
justments are made primarily through scheduling overtime labor hours. In order to make sure that customer orders can be turned around in less than a day Žmore often than not., the shop schedules more labor hours than the average daily processing requirement. Clearly, the financing of large raw material inventories and the excess production capacity that results from the large amount of uncertainty increases the total supply chain cost. If customers were given an incentive to share information about their requirements with the distributor, there would be opportunities to reduce inventories and to operate at a lower capacity level. By offering customers a discount for committing to their orders in advance, the distributor would encourage buyer behavior that would reduce its own costs. As long as the discount is less than the amount by which its own costs would be reduced, the distributor would be better off. Assuming, of course, that the customers respond to the discount in a rational, self-interested manner, they too might be better off, but would certainly be no worse off. In Section 4, we quantify the amount by which the distributor’s costs would be reduced by various levels of advanced commitment from their customers and then express the cost reduction in the form of a price discount.
4. Model of supply chain costs At the distributor we studied, the demand is created by a relatively large number Ž) 20. of independent customers, each of whom may place more than one independent order per day. The orders placed tend to be small, often requiring only one coil. As a result, the demand can be modeled as a Poisson
process, and the demand during any time interval can be modeled as a Poisson random variable. This model would not be appropriate for situations in which the demand is generated by a few large orders. In the discussion to follow, the terms orders and coils are used inter-changeably, implicitly assuming that each order is for exactly one coil. It is well known that the Poisson distribution can be approximated by a normal distribution when the parameter representing the mean is large. At the steel distributor with which we interacted, the total demand averaged about 60 coilsrday. Thus, the total demand during a time interval of 1 or more days can be approximated by a normal distribution. We denote the mean and standard deviation of the total demand for coils during a period of length L days as Ld tot and 'L s tot , respectively. This demand is composed of requests for n different coil types, and for the most part, these demands are independent of one another. To avoid adding unnecessary complexity, we assume that the distribution of daily demand for each of the n different coil types has mean d s d totrn and standard deviation s s s totr 'n . Note that although the normal approximation may be relatively crude when d s d totrn is very small, it allows us to employ standard inventory models to understand the basic tradeoffs. Under the current mode of operation, customers make almost no advanced commitment to specific shipment timing or quantities. Although some customers do provide preliminary lists of what and when they plan to purchase, there is no incentive to adhere to the expected release dates for these quantities. They frequently change them to better meet their own production requirements. As a result, it is difficult for the distributor to optimize its own operations based on these shifting, uncertain demands.
S.M. Gilbert, R.H. Ballour Journal of Operations Management 18 (1999) 61–73
However, if customers could be convinced to commit to their orders prior to the date upon which they require delivery, then operational exposure to uncertainty could be reduced. Let us suppose that, for some fraction of demand, advanced commitment can be obtained a certain length of time in advance of required delivery. In particular, assume that the fraction b of all demand is ‘‘committed to’’ Lc time units in advance of when delivery is required. Throughout the remainder of the paper, demand for customers providing advanced commitment will be referred to as committed demand, and demand for which no such advanced commitment is provided will be referred to as regular demand. In the following sections, we develop models for quantifying the amount by which the costs of raw material inventory and excess capacity are reduced when a fraction b of demand is committed Lc time units in advance. 4.1. The effect of prior ordering commitments upon raw material inÕentory costs Given the above characterization of the demands for each coil type, we can develop a model of the effects of advanced commitments from customers upon raw material inventory costs by making an appropriate modification to a traditional continuous review re-order point inventory model. ŽAt the steel distributor, purchasing is based on a continuous review re-order point policy.. As described below, the modification involves the determination of the standard deviation of lead time demand as a function of the proportion of committed customers and the length of their commitment. Let S be the ordering cost that is incurred each time the distributor places an order for one of the n coil types Žitems.. Let h be the cost of holding one unit of inventory for 1 day, and assume that it is the same for all coil types. At the distributor with which we interacted, customers tend to have more than one source of supply. If one supplier is out of stock on a particular item, they can generally obtain it elsewhere. Therefore, it is assumed that if demand for a given item occurs while the distributor is out of stock on that item, then the demand is lost. Let k be the cost of each unit of lost demand. The lead time from the steel mills Žthe supplier to the distributor. is
65
Ls . For purposes of illustration, we assume that the length of supply lead time Ž Ls . is deterministic. In order to determine the optimal continuous review Ž s,S . inventory policy, the demand distribution that is appropriate for each of the n items during the lead time must first be characterized. To do this, the regular demand will be analyzed separately from committed demand. The daily demand of regular customers for each of the n items is approximately normally distributed with mean d r s Ž1 y b . d and standard deviation sr s s Ž 1 y b . . Therefore, using standard probability theory results, the regular demand during the lead time is normally distributed with mean and standard deviation:
(
d L r s Ž 1 y b . dLs
(
(
sL r s sr 2 Ls s s 2 Ls Ž 1 y b . s s Ls Ž 1 y b . .
(
Ž 1. The daily committed demand has mean d c s b d and a standard deviation sc s s b . However, for the committed demand, the distributor is not exposed to demand uncertainty over the entire length of the raw material supply lead-time from the mill. As depicted in Fig. 2, at the time that the distributor orders raw material from the steel mill, it has already received all information about committed demand that will need to be satisfied within the next L c time units. Therefore, it knows with certainty how many coils it will have to ship to satisfy committed demand during the next L c time units. This is the benefit of advanced commitment. However, at the time it orders raw material from the mill, the distributor has not yet been informed as to the amount of committed demand that will need to be satisfied during the last Ls y Lc units of time during the raw material lead time from the mill. Therefore, as shown in Fig. 2, the distributor is exposed to the uncertainty of committed demand during the interval labeled as Ls y Lc .
'
Fig. 2. The distributor’s exposure to demand uncertainty from ‘‘committed’’ customers during an order cycle.
S.M. Gilbert, R.H. Ballour Journal of Operations Management 18 (1999) 61–73
66
To formalize this, let t be a point in time at which an order is to be placed with the steel mill, and let x t be the number of outstanding committed orders at time t. In other words, at time t, it is known that exactly x t coils must be shipped to satisfy committed demand during the next Lc time units. In addition to this known demand, there is also the unknown portion of committed demand that will have to be satisfied during the lead time. This unknown portion of committed demand consists of the requests that are received from customers after the raw material is ordered from the mill, but that also need to be satisfied before the raw material is received from the mill. It is normally distributed with mean d c Ž Ls y L c . and standard deviation sc Ls y Lc . Recall that d c s b d and sc s s b . Therefore, by substituting for d r and sr , the total committed demand that needs to be satisfied during the supply lead time is normally distributed with the following mean and standard deviation:
(
'
d L c s x t q b d Ž Ls y L c .
(
sL c s s b Ž Ls y L c .
where Q is the order quantity, and EŽ z . is the unit normal loss function. Setting the derivatives of C with respect to Q and z to zero yields: QU s
(
2 d Ž S q k sL E Ž z . . h
PU s
kd Qh q kd
Ž 5.
where P U is the optimal probability with which there is a stockout in a given replenishment cycle. Note that for a given value of P U , the corresponding value of z can be found in a table of the cumulative standard normal distribution. Therefore, an iterative procedure can be used to solve for QU and P U . By substituting these optimal values back into Eq. Ž4., the optimal cost of ordering and stocking the raw material for each of the n items for any combination of Lc and b can be calculated. Note that the above model is not specific to the steel distributor that we observed. Indeed, it can be applied to any item that is managed by a continuous review inventory policy and for which the demand can reasonably be modeled as a Poisson process.
Ž 2. The regular and committed demand can now be combined to see that the total demand during the lead time is normally distributed with the following mean and standard deviation: d L s x t q b d Ž Ls y Lc . q Ž 1 y b . dLs s x t q d Ž Ls y b L c .
Ž 3a .
( s s(L y b L
Ž 3b .
sL s s b Ž Ls y L c . q Ls Ž 1 y b . s
c
A traditional approximate cost model for lost sales can now be developed to analyze the total cost per day for procuring and stocking raw materials for each of the n items. Average cost per day s ordering cost q shortage cost q holding cost Ž regular andsafety stock . Cs
d Q
Sqh
ž
Q 2
/
q sL E Ž yz . q
d Q
k sL E Ž z . Ž 4 .
4.2. The effect of prior ordering commitments upon the cost of excess capacity The uncertainty about customer requirements may also make it necessary to maintain large amounts of excess capacity in production equipment, labor force, and storage space. However, if some customers provided advanced commitment, it would be possible to smooth the rate of production. Hence, less total production capacity would be needed to satisfy customers’ needs in a timely fashion. Consider the following situation for 2 consecutive days: Suppose that on the first day there is less demand than can be met with the scheduled capacity, and that on the second day there is more demand than can be met with the scheduled capacity. In the current mode of operations, workers will be idle for part of the day on the first day, and orders would either be late or go unfilled on the second day. Alternatively, if some of the customers for the second day had given advanced commitment, their orders could have been processed on the first day, freeing up capacity for other customers later on.
S.M. Gilbert, R.H. Ballour Journal of Operations Management 18 (1999) 61–73
The above example demonstrates how advanced commitment from customers allows a make-to-order firm to smooth its production rate. To approximate the way that advanced customer commitments affect the amount of excess capacity that is needed, we use a simple queuing model. Let us denote the expected amount of time between the receipt of a customer order and the completion of its processing by W. We assume that in order to insure that due date commitments can be filled, management maintains enough capacity so that, the average time ŽW . within which an order can be filled is no larger than some fraction Žwhich we denote by c . of the quoted lead time. For example, if customers are being quoted a lead time of L time units, then we assume that processing capacity must be sufficiently large that the expected time to complete an order is W s c L. For simplicity, we assume that processing times are exponentially distributed and that the arrival of orders is a Poisson process. This allows us to analyze the workload on each machine as an MrMr1 queue. Although actual processing times are not exponentially distributed, this approach allows us to develop a simple model that provides insight as to the general tradeoff between advanced commitment and the amount of excess capacity that must be maintained. Recall, from standard results for an MrMr1 queue, that for a given rate of demand Ž l. and processing capacity Ž m ., the expected time to complete an order ŽW . can be expressed as follows: Ws
myl
W s b Wc q Ž 1 y b . Wr
1
c Lr
Ž 8.
To make sure that the expected turn-around time for regular customers is no larger than Wr F c L r , recall that under the assumed queue discipline, orders from committed customers are never allowed to interfere with the processing of regular customers orders. Therefore, expected turn-around time for regular customers depends only on the arrival rate of regular customers, and is independent of the arrival rate of committed customers. Therefore, for any given amount of capacity Ž m ., we have: y1
Ž 9.
Ž 6. Thus, in order to make sure that we have adequate capacity to satisfy regular customers, we need:
Thus, given Lr , l, and c , we can easily compute the amount of capacity that is required if all orders must be filled within the same Žregular. lead time.
mGlq
advantage of this flexibility would be to assign these orders lower processing priority. Therefore, let us assume that two queues are maintained: one for committed customers and one for regular customers. Within each queue, orders are processed first-comefirst-served, but regular customers are always given priority over committed customers. Let us denote the required expected turn-around time for regular and committed customers by Wr and Wc , respectively. Note that because the distribution of processing time does not depend on the type of customer, this processing scheme will not change the overall average expected time ŽW . to complete an order for a given level of capacity Ž m .. It will simply allow the regular customers’ orders to be finished faster at the expense of committed customers. Thus, for a given level of capacity m :
Wr s Ž m y Ž 1 y b . l .
1
67
Ž 7.
Now suppose that some fraction b of orders can be completed in a longer lead-time of Lc . To analyze how this affects the amount of capacity that is required, note that the longer lead time for committed customers affords a certain amount of flexibility in the processing of these orders. One way to take
mG Ž1yb . lq
1
Ž 10 .
c Lr
At the same time, we need to make sure that we have enough capacity to provide an expected turnaround time for committed customers of no more than c Lc . By substituting Eqs. Ž6. and Ž9. into Eq. Ž8. and solving for Wc , we have that, for a given amount of capacity Ž m .: Wc s
1
ž
1yb
1
b myl
y
my Ž1yb . l
/
Ž 11 .
S.M. Gilbert, R.H. Ballour Journal of Operations Management 18 (1999) 61–73
68
Thus, in order to make sure that we have adequate capacity to satisfy committed customers, we need to have adequate capacity to insure that Wc F c Lc . Substituting this inequality into Eq. Ž11. and performing some algebraic manipulations, we get:
mG
1 2 c Lc
ž Ž 2 y b . lc L q1
(
c
2
q Ž lc Lc b q 1 . q 4lc Lc Ž 1 y b .
/
Ž 12 .
We need to make sure that we have sufficient capacity to satisfy constraints Ž11. and Ž12., in order to satisfy our regular and committed customers, respectively. The total amount of capacity that we need for any combination of l, L r , Lc , c , and bc is the maximum of the right hand sides to these two inequalities. Note that this model is a somewhat abstract representation of the actual capacity requirement. This is due to its assumptions of exponentially distributed processing times, its emphasis on expected turnaround times, and the fact that it assumes that regular customers are given absolute priority over committed customers. However, in spite of these limitations, the model does represent the general effect that increased processing flexibility from committed customers can have on the amount of capacity that is required.
5. Typical results In order to illustrate how our model can be used, we draw upon data that is representative of the steel distributor that motivated this work. In particular, there are about 250 different types of coils that must be processed. We estimated the mean and standard deviation of daily demand to be about d tot s 60 and s tot s 7.8, respectively. ŽNote that this implies a coefficient of variation that is consistent with a Poisson process.. For simplicity, we assumed that this demand is spread uniformly across the 250 coil types, so that the daily demand for each coil type has mean d s 0.24 and s s 0.5. Based on the potential for lost profits, stockout costs Ž k . were estimated to be US$243rcoil. Holding costs were estimated based on the opportunity cost of capital. Since the average
cost of a coil is about US$2000, and the annual cost of capital is approximately 25%, we took h s US$2 per unit per day. On average, raw material lead time from the mills is about 8 weeks, so we assume Ls s 40 days. To estimate the order processing cost, we observed that each time an order is placed, long-distance telephone calls are made to suppliers to check stock availability, delivery times, and prices, hourly clerical personnel need to be compensated for the time that they spend, and a shipping charge is incurred based on the order size. Based on these events, we estimated Žconservatively. the order processing cost to be S s US$50rorder. Each of the eight machines in the shop can process about eight coils in an 8-h shift. Although between one and three workers are typically needed to operate a machine, we assume that exactly two workers are needed for each of the machines. Recall that each machine performs a slightly different function, therefore, each customer order must be processed on a specific machine. For simplicity, we assume that the average rate of demand is the same for all eight machines. In particular, we assume that the demand processed on each machine is a Poisson process with rate l s d totr8 s 7.5 coilsrday. Currently, the shop schedules about 1.5 h of overtime per day at each machine. Based on the model presented in Eq. Ž7. this implies that c s 0.5. The operators are paid US$18rh for regular shift, and US$24rh for overtime, including benefits. Since union rules preclude scheduling less than a normal 8-h shift, we define excess capacity as the amount of overtime labor that needs to be scheduled. Each machine requires an average of two operators. Therefore, the cost of excess capacity on each machine is US$48rh. With this information, our model can be used to estimate the supply chain costs for various fractions of committed customers Ž b . and the number of days in advance that committed customers give for their orders Ž Lc .. The results of our model are shown in the graphs of Fig. 3. Fig. 3a and b show separately how the annual costs associated with raw materials and excess capacity are affected. As should be expected, both costs decrease in the fraction of demand that is committed in advance. What is perhaps more interesting is the way in which the costs decrease. Since raw material costs tend to be concave in b , the
S.M. Gilbert, R.H. Ballour Journal of Operations Management 18 (1999) 61–73
69
vance notice Ž b s 0., the combined cost of holding raw materials inventory and excess capacity is US$1,179,000 per year. On the other hand, if 50% of the customers commit to firm orders just 6 days in advance of processing Ž Lc s 6., the company can realize an annual cost reduction of US$1,179,000 y 1,026,214 s US$152,786. As can be seen from the graph, the higher the fraction of demand that is committed and the longer the length of time commitment, the greater the potential cost reduction is for the steel distributor. Obviously, the maximum cost reduction is achieved when all orders are placed at least 40 days in advance of processing. Commitments longer than the replenishment lead time from the steel mills offer no further advantage to the steel distributor. The value of the chart in Fig. 3c is that it provides a tool for aligning pricing policy with operating costs. By communicating the cost implications of various levels of commitment from customers to sales representatives, it becomes possible to develop pricing policies that are more consistent with operating costs.
6. Generating a pricing policy
Fig. 3. Ža. Annual raw material inventory costs as a function of the fraction of the customers committing to firm orders Ž b . and the time in advance of processing Ž Lc . in days. Žb. Annual cost of excess capacity Žovertime. as a function of the fraction of the customers committing to firm orders Ž b . and the time in advance of processing Ž Lc . in days. Žc. Combined annual cost of inventory and excess capacity as a function of the fraction of the customers committing to firm orders Ž b . and the time in advance of processing Ž Lc . in days.
incremental cost reductions become larger as more demand is committed. In contrast, since the costs of production schedule changes tend to be convex in b , the incremental cost reductions become smaller as more demand is committed. Fig. 3c shows the magnitude of the combined annual cost reductions for this particular configuration of costs, demand, and lead times. In the current mode of operation where no customers provide ad-
Customers currently provide little advanced information about their requirements. Even though customers may know far in advance that they will need a certain number of coils of a particular coil type on a specific date, there is currently no incentive for them to provide this information to the steel distributor. These same customers apply nearly constant pressure on the distributor to reduce prices, resulting from their own cost reduction programs and the competitive nature of the undifferentiated service that the distributor provides. Unfortunately, the steel distributor has limited ability to reduce the prices without reducing operating expenses, as prices already reflect the current state of order uncertainty. As discussed in Section 5, one way for the steel distributor to reduce its costs is by obtaining advanced commitment from customers. Although this sort of advanced commitment reduces the customers’ flexibility, not all customers require the same amount of flexibility to change their orders. A single customer may not even require the same amount of
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S.M. Gilbert, R.H. Ballour Journal of Operations Management 18 (1999) 61–73
flexibility for every coil ordered. For example, suppose that a customer has planned a production batch that requires two to four steel coils, the exact quantity to be determined on the production date. Since this customer will certainly need at least two coils, an order is submitted for two coils, while allowing flexibility to order the other one or two at a later time. Note that under the current policy, all customers pay for infinite flexibility for every coil. Therefore, many customers will likely provide advanced commitment to at least some of their orders in return for a lower price per coil. This seems reasonable since customers seek lower prices on a highly substitutable service as long as the price reduction exceeds the disadvantage of less ordering flexibility. 6.1. A conceptual approach to pricing policy In order to develop a pricing policy, we would need to estimate the responsiveness of customers to various levels of discounts and lengths of commitment. To illustrate, suppose that a discount will be offered for a single level of commitment. Let p be the percent discount that is applied to each coil to which a customer provides advanced commitment. The fraction of demand that is committed in response to a given discount depends upon both the magnitude of the discount and the length of commitment. Thus, we can represent this fraction as a function b Ž p, Lc . which can reasonably be assumed is increasing in p and decreasing in Lc . Although the sales staff may have some intuition about the general shape of this function, it is likely that some experimentation would be necessary in order to quantify it. When a discount is offered, both the distributor’s revenue and costs will be affected. Let RŽ p, Lc . be the distributor’s revenue when a discount of p percent is offered to customers agreeing to provide commitment to their orders L c time units in advance. Denoting the distributor’s current revenue by R, this function can be expressed as: R Ž p, Lc . s Ž 1 y pb Ž p, Lc . . R
Ž 13 .
Note that this revenue function implies that the only effect of the discount upon demand is to encourage
customers to make advanced order commitment, where the total magnitude of demand is unaffected by the discount. This is consistent with Lal and Staelin Ž1984., Monahan Ž1984., Banerjee Ž1986. and Lee and Rosenblatt Ž1986., and is reasonable when the output levels of downstream customers are relatively insensitive to their costs associated with this particular input. To the extent that this assumption is not valid, we would need to include a stimulation effect in Eq. Ž13.. Fig. 3c depicts the distributor’s costs as a function of committed customers. Denote this relationship as C Ž b , Lc .. Once the function b Ž p, Lc . has been estimated, the distributor’s costs can be expressed as C Ž bc Ž p, L c ., L c .. From Fig. 3c, it can be observed that C Ž. is decreasing in both of its arguments. For a given length of commitment, b Ž p, L c . is increasing in p. It follows that C Ž b Ž p, Lc ., Lc . is decreasing in p. The distributor’s profit can be expressed as the following function: Profit Ž p, L c . s R Ž p, Lc . y C Ž b Ž p, Lc . , Lc . Ž 14 . The optimal pricing policy can be identified by optimizing first with respect to p, and then with respect to L c . In general, maximizing Eq. Ž14. with respect to p for a given L c is not easy because it is not necessarily concave, or even unimodal. However, in many industrial markets, there are classes of customers that face similar cost tradeoffs and might be expected to respond similarly to one another. In such a case, for a given value of L c the function b Ž p, Lc . will resemble a step function, greatly simplifying the process of identifying the optimal discount pU Ž L c . for a given lead time. Assuming that only one combination of discount and length of commitment is to be offered, then need is only to compare ProfitŽ pU Ž L c ., Lc . across the range of Lc . 6.2. A pragmatic approach to deÕeloping a pricing policy In order to develop a pricing policy that is mutually beneficial to both the distributor and the downstream customers, the results shown in Fig. 3c can be drawn upon. From our example, regular customers are currently charged a price of US$2500rcoil. Given that the average daily demand is 60 and there are
S.M. Gilbert, R.H. Ballour Journal of Operations Management 18 (1999) 61–73
250 working days per year, the average annual demand is 15,000 coils. Suppose that a price reduction is offered on each coil for which customers give 40 days advanced notice. If a target number of 50% of coils will be ordered with advanced commitment, the maximum cost reduction to be realized by the steel distributor is US$1,179,000 y 869,000 s US$310,000 per year. Since 50% of the 15,000 coils are expected to be affected by the cost reduction, the savings per coil is US$310,000r7500 s US$41.33. This is approximately 8% of the value added by the steel distributor Ž20% = US$2500.. This is the maximum price reduction that can be offered to entice 50% of the customers to commit to their orders 40 days in advance. If these customers can be enticed with a smaller price reduction, then the distributor will be better off. Since the company does not now price in this fashion, it is not known how customers will respond to the price incentive. That is, the fraction of orders that will be committed is not known for a particular price reduction amount. However, experimenting with different price reductions for various commitment times will give the likely fraction of committed orders to result from a given price discount level. The price incentive can be refined so that b , Lc , and the price reduction are in conformance. The economics expressed in Fig. 3c provide the basis for determining the effective price discount. That is,
71
when the price sensitivity of the customer is generally understood, Fig. 3c can be reviewed to see if the price reduction being offered does not exceed the maximum allowed. Ideally, there exists a discount less than the distributor’s maximum for which an appropriate portion of buyers would benefit from commitment. If so, both the committed customers and the distributor are better off. On the other hand, because customers can reject the discount and continue buying as they always have, none of them will be any worse off after the discount is offered. Example. Table 1 represents the maximum percent price discount that can be offered to induce various amounts of commitment as measured by b and L c . Lower price discounts may actually be offered so that the distributor benefits as well. For a given combination of b and Lc , the table represents the average savings in raw materials and excess capacity costs per committed coil expressed as a fraction of price. Using our previous notation, it is generated by taking C Ž b , Lc . y C Ž0,0., which can be obtained from Fig. 3, and dividing this cost savings by the number of committed customers. This per-coil saving is then divided by the coil list price. Once the customer response to price is approximately known, the body of the table can be searched for a price discount schedule that offers different price discount levels for various advanced commitment times. To obtain 12 days of commitment from 60% of the orders, the distributor can offer a dis-
Table 1 Maximum percent price discount that can be offered for various advanced customer order commitment times Fraction of committed customers, b
Advanced commitment Ž Lc . in days 0 6 12
24
32
40
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
2.32 2.38 1.76 1.44 1.26 1.14 1.06 1.00 0.96 0.94
2.50 2.54 1.92 1.62 1.42 1.34 1.28 1.24 1.24 1.24
2.68 2.70 2.10 1.80 1.66 1.58 a 1.54 1.56 1.62 1.98
a
1.64 1.24 1.04 0.92 0.82 0.74 0.66 0.60 0.54 0.50
2.10 1.96 1.50 1.20 1.00 0.88 0.78 0.72 0.66 0.64
Example calculation: From Fig. 3c, the cost for b s 0.6 and L c s 0 is US$1,179,000 and for b s 0.6 and Lc s 40 is US$825,000. Total savings is US$1,179,000 y 825,000 s US$354,000. Coils affected are b = 15,000 or 9000. Savings per coil is US$354,000rŽ0.6 = 15,000. s US$39.33. Percent price reduction is Ž39.33rUS$2500. = 100 s 1.58%.
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count of up to 0.88%. On the other hand, to obtain 40 days of commitment from 60% of the orders, the distributor can offer a discount of up to 1.58%. If more customers wish to take advantage of the price discount than the fraction b associated with a particular price, it may be necessary to limit the availability of the discount or to adjust the amount of the discount until it is balanced with b . Although the percentage discounts in this example appear to be small, they are not necessarily insignificant, particularly for customers in highly competitive industries where a large portion of the cost of goods sold is represented by steel purchases. For example, consider a customer for whom profit margins are 10% and steel costs represent 80% of sales. Even a discount of 1.0% off of all its purchases represents an 8% increase in profits. Moreover, if the discount offered is not large enough for a particular customer to change its order commitment patterns, the customer simply stays with the current, flexible order pattern. Although neither party realizes any benefit from this action, neither one is worse off when customers continue their current ordering-pricing practices. The example illustrates how the results of this research might be used.
7. Conclusions In this paper, a situation has been described in which the failure to obtain reliable advanced notice about customer requirements has resulted in some cost inefficiencies for a steel distributor. For this particular firm, the inefficiencies involved raw material inventories and excess production capacity. Although the specific sources of inefficiency may differ from one firm or industry to another, there are many opportunities to eliminate inefficiency in the supply chain by creating incentives for downstream members to provide advanced notice to their upstream partners about their needs. A general concept has been provided and some price discount bounds for a supplier to use advanced order commitments as a means of offering lower prices. There is little research to indicate that advanced order commitments has been studied as a basis for price discounting. We hope that this work provides some initial insights that will lead to further research in this area.
Like many firms, the steel distributor that was studied followed an industry norm Žthat of allowing customers infinite flexibility to place or change their orders. without carefully considering the implications of this practice. Since this practice drives up the marginal costs in the industry, it creates an opportunity for a firm to offer slightly less flexibility to customers in the form of early order commitment, in exchange for lower prices. However, it is only by understanding the cost implications of advanced ordering that a firm can offer price incentives benefiting both itself and its customers. The model presented provides a useful tool for estimating the cost savings associated with various levels of advanced order commitment. Although the focus on the costs of raw materials and excess capacity is specific to the steel distributor that motivated this research, the general approach can be applied to a wide variety of firms. Even though the specific nature of cost implications may differ from industry to industry, there are many opportunities for firms to offer their customers price reductions in return for early order commitment. It has been demonstrated that industrial firms can quantify the cost reductions associated with early commitments from customers, paving the way for new pricing policies that benefit both themselves and their customers.
References Banerjee, A., 1986. A joint economic-lot-size model for purchaser and vendor. Decision Sciences 17 Ž3., 292–310. Emmons, H., Gilbert, S., 1998. The role of returns policies in pricing and inventory decisions for catalogue goods. Management Science 44 Ž2., 276–283. Jeuland, A., Shugan, S., 1983. Managing channel profits. Marketing Science 2 Ž3., 239–272. Lal, R., Staelin, R., 1984. An approach for developing an optimal discount pricing policy. Management Science 30 Ž12., 1524– 1539. Lariviere, M., Porteus, E., 1995. Informational dynamics and new product pricing. Stanford University Working Paper. Lee, H., Rosenblatt, M., 1986. A generalized quantity discount pricing model to increase supplier’s profits. Management Science 33 Ž9., 1167–1185. Moinzadeh, K., Ingene, C., 1993. An inventory model of immedi-
S.M. Gilbert, R.H. Ballour Journal of Operations Management 18 (1999) 61–73 ate and delayed delivery. Management Science 39 Ž5., 536– 548. Monahan, J.P., 1984. A quantity discount pricing model to increase vendor profits. Management Science 30 Ž6., 720–726. Paternack, B.A., 1985. Optimal pricing and return policies for perishable commodities. Marketing Science 4 Ž2., 166–176.
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Raturi, A.S., Meredith, J.R., McCutcheon, D.M., Camm, J.D., 1990. Coping with the build-to-forecast environment. Journal of Operations Management 9 Ž2., 230–249. Weng, Z.K., 1995. Channel coordination and quantity discounts. Management Science 41 Ž9., 1509–1522.