- Email: [email protected]
Materials receiving capacity and inventory management
OMEGA Int. J. of Mgmt Sci., Vol. 19, No. 6, pp. 559-566, 1991 Printed in Great Britain. All rights reserved
0305-0483/91 $3.00 + 0.00 Copyright © 1991 Pergamon Press plc
Materials Receiving Capacity and Inventory Management JF CAMPBELL K JOSHI University of Missouri-St Louis, USA (Received April 1990; in revisedform February 1991) This paper analyses the optimal level of materials receiving capacity for a manufacturer that receives deliveries from many suppliers. Inventory levels and inventory carrying costs depend on the frequency of deliveries and thus, on the materials receiving capacity. An analytic model that captures the tradeoff between inventory costs and materials receiving costs is presented and discussed. The receiving cost is modeled as increasing in discrete jumps of varying sizes whenever materials receiving resources are added. Practical issues in implementing the model are highlighted and methods to reduce the marginal materials receiving cost are discussed. The paper also discusses connections to the ,liT approach for production environments where materials receiving is heavily automated.
Key words--inventory control, just-in-time, EOQ
INTRODUCTION MATERIALS management encompasses issues in a variety of areas, including inventory management, purchasing, warehousing, materials handling, transportation and customer service, Although much research has focused on inventory management decisions involving order quantities, reorder points and safety stocks, decisions involving the materials receiving process have received less attention. Determing the amount of materials handling equipment that should be installed, the number of employees that should be assigned to processing deliveries, and the nature and degree of automation in handling deliveries are important decisions for many organizations. A fundamental question for the materials receiving process is: "What should be the overall materials receiving capacity?" Although the materials receiving capacity can be viewed as fixed in the short-term, it may vary in the long-term with the addition and deletion of materials receiving resources (e.g. materials 559
handling equipment, labor, documentation and inspection capabilities and facilities, etc.). Determining the optimal materials receiving capacity helps to determine the optimal level of these resources. Increasing the receiving capacity may be expensive, but it permits more frequent deliveries, which reduces the average inventory levels and, consequently, the inventory carrying costs. This paper analyses the tradeoff between the cost of increasing the materials receiving capacity and the cost savings from reduced inventories. Items delivered to an organization can often be classified as either regularly consumed items or special items. Regularly consumed items are those common to many products, so there is generally a high demand for these items. Special items are those needed for special products and consequently have a low demand. This paper focuses on the regularly consumed items delivered to a manufacturer. In high volume mutli-product production environments, many of the items are regularly consumed items cornmort to all or most of the products. Even in job shops, many of the items, such as hardware,
560
Campbell, Joshi--Materials Receiving Capacity and Inventory Management
bearings, electrical components, etc. tend to be common to many products, The annual demand for regularly consumed items can often be estimated based on past data, so that annual orders can be placed with suppliers. Annual ordering benefits the manufacturer by providing leverage to negotiate better prices and reducing the order cost and effort. Annual ordering benefits the supplier as well, by providing large orders and advance notice, The second author's experience with a number of companies indicates that annual ordering of regularly consumed items is a common practice. Once annual orders are placed, delivery frequencies must be specified for each item. Delivery frequencies may be adjusted periodically (e.g. monthly) to better meet demand. This paper determines the optimal materials receiving capacity for regularly consumed items delivered from a number of different suppliers. This paper considers those items for which the consumption pattern and annual demand can be estimated, so that annual orders are placed, The traditional EOQ model could be used to determine an optimal delivery quantity and thus, an optimal delivery frequency, for each item separately. Summation of the individual EOQ delivery frequencies yields a total delivery frequency or capacity. However, there are some difficulties with this approach. The difficulty in accurately estimating and assigning order costs to individual items is well known [11, 16]. In purchasing environments with long term (e.g. annual) order contracts, the ordering costs are already sunk and therefore are not relevant for future delivery decisions. The incremental cost for receiving a delivery is relevant for the EOQ analysis. However, even this cost may be difficult to estimate. Another problem is that the receiving capacity provided by a set of resources may exceed the capacity that results from summing the individual item EOQ delivery frequencies. Inventory costs could then be reduced by increasing the delivery frequencies above the EOQ levels to fully utilize the available receiving capacity, An additional problem with determining a total receiving capacity by summing the individual EOQ delivery frequencies results from the implicit assumptions that the marginal cost of receiving an additional delivery is constant and that receiving capacity can always be added in small increments. These assumptions imply that the cost for receiving deliveries is a linear
function of the receiving capacity. However, materials receiving resources are often acquired in discrete units (e.g. one fork-lift or one worker). Thus, the cost for receiving deliveries is a discontinuous function of the receiving capacity that increases in discrete jumps when resources are added. This paper analyses the tradeoff between materials receiving costs and inventory costs to determine the optimal materials receiving capacity by considering the items received in aggregate, instead of separately. Neither the EOQ model nor this paper explicitly consider transportation costs. The inventory management approach suggested in this paper consists of two steps. The first step, which is to determine the optimal receiving capacity, is the subject of this paper. The second step, which is to divide the receiving capacity among the items in an optimal fashion, was addressed elsewhere [8]. The remainder of this paper is divided into five sections. The next section discusses materials receiving costs. The following section discusses the optimal total materials receiving capacity. The following section examines some practical issues and presents an example. The following section highlights the connection between the model presented in this paper and the JIT approach. The final section is a discussion of the paper and some limitations. MATERIALS RECEIVING COSTS The tasks required to receive a delivery can be divided into clerical tasks, materials handling tasks and quality assurance tasks. Each task requires certain materials receiving resources, and a given set of receiving resources provides a certain receiving capacity. For a given set of receiving resources, many of the receiving costs (e.g. salaries, equipment costs and overhead) are already sunk or committed. Therefore, these costs are largely independent of the number of deliveries. This paper addresses situations where the marginal cost of receiving an additional delivery is negligible, unless additional resources are required. Thus, the receiving cost increases in discrete amounts when resources are added. The cost and type of resources added depend on the level of receiving capacity that exists and the type of additional resources needed. Increasing the receiving capacity may involve adding
Omega, Vol. 19, No. 6
workers at relatively low cost or adding cranes or lift trucks at relatively high cost. The marginal cost to receive an additional delivery should generally be small in situations where there have been significant investments in automation and materials handling equipment and facilities. A later section discusses how the marginal receiving cost may be reduced through automation, computerization and the efficient design, organization and operation of receiving and storage areas, It is important that all three areas, clerical, materials handling and quality assurance, have the same receiving capacity for efficient operations. An area that has a much lower capacity than the others will serve as a bottleneck and limit the overall receiving capacity. Therefore, investments in each area should be based on balancing the materials receiving capacity of all areas, OPTIMAL TOTAL MATERIALS RECEIVING CAPACITY The Appendix presents a model of the inventory and materials receiving cost. The inventory cost is a decreasing function of the number of deliveries. The materials receiving cost is an increasing step function of the number of deliveries. The receiving capacity and the receiving cost increase in discrete jumps each time that receiving resources are increased. Increasing the receiving capacity allows more frequent deliveries, which lowers inventory costs, but it requires additional investments in manpower or equipmerit. The model captures the trade-off between the inventory and receiving costs to determine the optimal materials receiving capacity, This model is most applicable to organizations that receive large volumes, so that the materials receiving personnel and equipment are fully utilized for receiving and are not available for other activities. Thus, for a fixed receiving capacity, the receiving cost is fixed and the inventory cost is minimized by fully utilizing the available receiving capacity. Because the minimal total cost occurs when there is no excess receiving capacity (for a given level of investment), the optimal receiving capacity can be found by analyzing the total cost at the points which correspond to fully utilized receiving capacities. Figure 1 shows the inventory, receiving and total costs. The small steps in the receiving cost
a00 is0 160 140 120 t00 _
~ ~ ~ ~ Z s0 ca 60 ~ 40 20
o
561
u \
\
I
~
]
~
Receiving cost
_ ] ~"
I
~.......~Inventory cost
I
I
I
I
20 40 60 ao loo Number of deliveries (thousands) Fig. I. Inventory, receiving and total cost.
curve might correspond to adding workers, while the large steps could correspond to adding expensive equipment. The optimal receiving capacity can be found by analyzing the cost only at the points that are local minima of the total cost in Fig. 1. The receiving capacity that results from summing the individual delivery frequencies from separate EOQ analyses may not fully utilize this optimal receiving capacity and thus, may result in a larger total cost. PRACTICAL ISSUES The optimal delivery frequencies for each item (calculated as N~* in the Appendix) need to be adjusted based on practical considerations. The receiving capacity should generally be set to allow a safety cushion above the level of the average number of deliveries per day. Although attempts should be made to schedule deliveries to balance the workload throughout each day and week, there will likely be times when the short-term receiving capability must exceed the average. If only a fraction fl (0 < fl < l) of the receiving capacity is to be used on average, then the analysis in the appendix holds if the number of deliveries is multiplied by ft. The optimal delivery frequencies should be adjusted to sensible values that fit into natural business cycles, such as once a month (12 times per year), twice a month (24 times per year), once a week (52 times per year), twice a week (104 times per year), once a day (260 times per year), etc. Slight adjustments to the delivery frequencies should not increase the cost significantly, because of the inventory and receiving cost tradeoffs. In theoretical models, the inventory cost is halved when a given demand is delivered twice a day instead of once a day. From a practical
Campbell, Joshi--Materials Receiving Capacity and Inventory Management
562
financial standpoint, the inventory cost for an item which is received more than once a day should be no different than if that item was received only once a day, because finance charges generally apply in units of days, not fractions of days. However, transportation and storage space considerations may make a single daily delivery of bulky items undesirable. For example, delivering items with insignificant storage space requirements once per day instead of several times per day may not increase the actual (as opposed to theoretical) inventory cost. However, multiple daily deliveries may be required for bulky items for which one day's supply exceeds one delivery vehicle load. When the optimal dehvery frequencies are adjusted to account for practical considerations, additional receiving capacity may be freed up. This additional receiving capacity can then be reallocated to other items to reduce inventory costs. Adjusting delivery frequencies to practical values is illustrated in the following example, Assume that a manufacturer orders 1260 items which can be divided into 3 classes as follows: Class
i 2 3
Number of items
,4nnualexpenditure per item
IO 250
s5,ooo,ooo 75,000
1000
200
~
t so
~ ~ ~ ~ ~ o
160 140 120 too -80s0 -40 20 0
~
~
r
I
3
Deliveries/year
0.013SN 0.00170s
0.000438N
where N is the total number of deliveries received per year (to be determined), Suppose that the materials receiving cost curve is estimated by the following set of costs and capacities: Cost
Capacity
($ per year)
(deliveries/,veaQ
15,000 30,000 45,1300
9000 19,000 30,000
55,ooo 70,000 83,000 92,000
Receiving cost Inventory cost
I I I I I 20 40 60 80 100 Number of deliveries (thousands) Fig. 2. Costs for example.
The capacity values are the maximum number of deliveries per year for a given cost. Suppose that these capacity values have already been adjusted to allow a margin of safety. The inventory, materials receiving the total costs are plotted in Fig. 2 for this example. The optimal receiving capacity will occur at one of the local minima of the total cost function in Fig. 2. The optimal capacity and cost can be found graphically or by evaluating the total cost at the seven capacity values listed above. The minimum total cost is $117,129 which occurs for an annual delivery capacity of 42,000. The optimal number of deliveries per year for each class of items is then: Class
I 2
" ~
5,000
To keep the illustration simple, assume that each item in a class requires the same annual expenditure. Therefore, all the items in a particular class will have the same number of deliveries. Assume an inventory carrying charge of 20% per year. The optimal delivery frequency for each class can be computed from Equation (A4) in the Appendix: Class
.
42,00o 53,000 76,000 t0o,00o
Deliveries/)'ear
2I
579.6
3
18.4
71.4
Each of the ten items in Class 1 should be delivered approximately 580 times per year, or 2.2 times per day (assuming 260 days per year). However, it is more practical to deliver each Class 1 item two times each day, i.e. 520 times per year. Changing the delivery frequency for the 10 Class 1 items from 580 times per year to 520 times per year allows an additional 600 deliveries each year. Adjusting the delivery frequencies for Class 2 and 3 items to consume this excess capacity will reduce the total cost. The following set of adjusted delivery frequencies fit into regular business cycles and require an annual receiving capacity of 42,000. Class I 2 3
Deliveries/year 520 (two times each day) 78 (three times every two weeks) 17.3 (once every three weeks)
The deliveries should be scheduled over the weeks to balance the workload as much as possible.
Omega, Iiol. 19, No. 6
CONNECTIONS TO THE JIT APPROACH
563
Organizations that have adopted the JIT philosophy have found novel ways to reduce Just-in-time (JIT) production systems have production set-up costs, including tool re-design, revolutionized production and inventory man- faster clamping devices and work area reorganagement practices and helped many organiz- ization. Applying the same approaches and the ations to improve both productivity and quality same initiative to the receiving process could [13-15]. A fundamental tenet of JIT production result in achieving greater receiving capacities systems is to produce in small lot sizes. Major with smaller investments. Whether or not an benefits include smaller inventories (which results organization adopts the JIT approach, the marin less inventory investment and less space re- ginal cost of receiving a delivery may be reduced quired), reduced scrap and rework, less inventory by a variety of actions. The marginal cost of accounting, faster feedback on defects and higher clerical work involved in handling a delivery can quality. JIT manufacturers have tried to extend be substantially reduced through computerizthe JIT philosophy to their suppliers by encour- ation. Data input chores can be eliminated by aging suppliers to make many deliveries of small EDI (Electronic Data Interchange) or by introshipment sizes, ducing barcodes and delivery documents that can The model presented in this paper generally be read directly by optical scanners, Marginal provides a wide range of optimal delivery fre- materials handling costs can be reduced by autoquencies for different items because of the large mating materials handling and unpackaging differences in the annual consumption in dollars, and through efficient design of the unloading, In some mass production environments it may unpackaging, and inspection complex. Redesign be prudent to invest heavily in materials receiv- of packaging may reduce unpackaging costs. ing automation in view of the large volume of Marginal inspection costs can be reduced by deliveries to be received and the economies of adopting a suitable quality assurance approach scale in receiving. Automation of the receiving at the vendor. Redesign or reorganization of the process is one way to reduce the marginal receiving and storage areas may also lead to cost to receive an additional delivery. As the reduced receiving costs. marginal receiving costs are reduced, the optimal Gordon [4] describes the implementation of an receiving capacity shifts towards more frequent automated receiving system at United Stationers, deliveries, the largest wholesaler of office products in the Extensive automation of the receiving process United States. A key to implementation was generally requires large initial costs for equip- computerization of many of the receiving activiment and facilities, but reduces the marginal ties previously done manually. Prior to autocosts for receiving additional deliveries. Auto- mation, receiving was done with a log book and marion of the receiving process is advisable telephone and shipments were never received when the volume of deliveries received is large against purchase orders. After automation, supenough that the marginal cost savings with auto- pliers or carriers were instructed to call for a mation exceed the initial costs for equipment delivery appointment. Deliveries were scheduled and facilities. If the receiving capacity is very and purchase order information was made availlarge, then the delivery frequency for each item able to check against the arriving shipments. The should be increased to its maximum level in computer system even provided instructions order to minimize inventory costs. When delivery for storage locations to maximize efficiency. frequencies are very high (e.g. at least once each Bar coding was used extensively and hand-held day), then the delivery schedule will approach laser scanners and thermal label printers were that for a JIT system. The model presented in acquired for maximum flexibility. Thirteen this paper shows that lower marginal receiving major distribution centers, each averaging costs result in larger optimal receiving capacities. 250,000 square feet, were automated over a one The extreme case of the model in which marginal year period. receiving costs are negligible indicates the desirObviously, considerations and costs other than ability of a JIT receiving process. If receiving receiving play very important roles in YIT sysand transportation costs are fixed, then JIT terns. Consolidation, economies of scale, and receiving with the smallest feasible shipment size considerations of transportation and storage is optimal, space may dictate delivery frequencies for some
564
Campbell, Joshi--Materials Receiving Capacity and Inventory Management
items [1]. For example, in a television manufacturing plant, picture tubes may be delivered more than once per day, while a small washer may be delivered once every two days or once a week. The role of transportation in JIT systems has been studied from a number of perspectives [2, 6, 7, 10]. The lack ofreliable on-time delivery has been perceived as a major impediment for JIT implementation [3]. As delivery frequencies increase, transportation reliability and cost become more important and the benefits of haying suppliers located close to manufacturers are obvious. The model presented in this paper does not account for transportation costs. Thus, it is most appropriate for situations in which receiving costs are more important than transportation costs, Clearly, JIT systems are not the answer in all situations. For small and medium sized organizations that do not have a mass production environment or a large enough operation, it may not be advisable to invest heavily in receiving automation to create a very large receiving capacity. In such a case, a strict JIT approach may not be optimal. For many manufacturers, a combination of JIT and MRP ideas may govern production and purchasing [9]. The model presented here provides insights for optimizing the investment in receiving capacity to minimize the total inventory costs in these environments, DISCUSSION The management of inventories remains an important activity with significant impacts on the profitability of an organization. This paper provides useful insights into the management of inventories and the optimization of materials receiving capacity. This paper relaxes some of the assumptions employed in the EOQ model by modeling the materials receiving cost as a discontinuous function of the receiving capacity, This paper optimizes the receiving capacity by examining the tradeoff between higher receiving costs and lower inventory costs, both of which result from higher delivery frequencies. The optimal receiving capacity provides a guideline for the investment in resources required for materials handling, inspection, document processing, etc. After the optimal receiving capacity is determined, it can be allocated among the many individual items to minimize inventory costs as shown in the example,
The model presented in this paper should be useful for organizations involved in job shop or batch oriented production, where there is generally an accumulation of inventories in the warehouse. On the other hand, in high volume production environments, under a JIT program, materials may be sent directly from receiving to the production lines, thus minimizing the accumulation of inventories and materials handling. In such mass production environments, control of flow and production efficiencies may require a high level of automation and elimination of receiving bottlenecks. This model is primarily applicable to job shop and batch production environments in which the accumulation of inventories decouples the issue of receiving efficiencies and production efficiencies. A limitation of the model presented in this paper is that transportation costs have not been considered. However, the model should be applicable when marginal unit transportation costs (with respect to frequency) are much less than the marginal receiving costs (assuming the mean and variance of lead time are independent of shipment size). The model is also applicable if the transportation costs per unit weight are independent of the shipment size (i.e. the frequency of deliveries). Finally, the steps needed to implement the model for items ordered on an annual basis are summarized as follows: (1) Estimate the existing receiving capacity in terms of the number of deliveries that can be handled annually. This may be based on the number of deliveries in the previous year, an estimate of the capacity utilization and any resources added since the previous year. Also estimate the annual consumption for each item and the inventory carrying costs. (Note that it is not necessary to estimate the reorder cost.) (2) Estimate the incremental costs involved in expanding the receiving capacity by small steps (e.g. a 2% increase). Plot or tabulate the costs and the corresponding receiving capacities. (3) Compute inventory costs associated with different receiving capacities based upon equation (A5). Add the inventory
565
Omega, Vol. 19, No. 6
COSTSto the receiving costs in the graph or table from step 2.
For a constant demand rate the average inventory value for item i is Ai/(2Ni) and the average inventory cost for all k items is C~(N):
(4) Identify the optimal delivery receiving capacity from the graph or table. (5) Allocate the optimal receiving capacity to individual items according to equation (A4). Note that estimation of the receiving capacities and costs in step 2 should usually include some safety margin to handle peak loads, which exceed the average load due to the inability to achieve completely balanced delivcry schedules. The possibility of diverting resources from other areas for short periods of time to handle peak loads should be considered in arriving at the safety margin for receiving resources.
APPENDIX This Appendix presents a model of the materials receiving and inventory cost for a manufacturer that receives k items from suppliers. Assume that if there are several items sent from one supplier they are consolidated to the extent possible into an item bundle, so that the term item below may refer to a bundle of items when appropriate, The materials receiving cost to receive N deliveries per year is C o ( N ) , which can be modeled as a step-function of the form CD(N)=M/
Rj_t
j=l,2 .....
(AI)
where the Rjs are the values at which the receiving capacity and cost increase, R0 = 0 and M / > Mj_ 1. Each value of Mj is the cost to provide receiving capacity of at least R~_ I, but not more then Rj deliveries per year. Define the following in order to formulate the inventory cost: A i -- annual dollar consumption for item i;
I = inventory carrying charge (% per year); Ni = delivery frequency for item i (deliveries per year); N = total delivery frequency for all k items,
C~N) = (I/2)~A,/N,, i=1
(A2)
where k
F. Ni = ,-1
(A3)
N.
Determining the optimal delivery frequency for item i was the focus of Joshi and Campbell [8]. Optimal delivery frequencies can also be found using Lagrange multipliers (e.g. Hadley and Whitin [5]) or using the LIMIT model (e.g. Plossl and Wight [12]). The optimal delivery frequency from [8] is: (A4) k )".x/~, ,-, From equations (A2) and (A4), the minimal inventory cost with a total of N deliveries per year, C~'(N), is N* = Nx/-~
CT(N)--~-~ Z
2.
(A5)
The sum of the inventory cost and the materials receiving cost is TC(N) = C~(N) + Co(N ).
(A6)
Because the inventory cost is a decreasing function of the number of deliveries, N, and the receiving cost is piece-wise constant, the total cost achieves a local minimum for each value of Rj. Thus, the optimal cost is min{TC(R/)}. j REFERENCES
1. Ansari A and Heckel J (1987) JIT purchasing: Impact of freight and inventory costs. J. Purchasing Mater. Mgrnt 23(3), 24-28. 2. Bagchi PK (1988) Management of materials under just-in-timeinventorysystem:A new look. J. Bus. Logist. 9(2), 89-102. 3. Cheng TCE (1988) The just-in-time production: A survey of its developmentand perception in the Hone Kong electronics industy. Omega 16(1), 25-32. 4. Gordon J (1990) A manual for automation.Distribution g9(2),48-54. 5. HadleyG and WhitinTM (1963) Analysis of Inventory Systems. Prentice-Hall, EnglewoodCliffs, NJ. 6. Hill AV and Vollman TE (1986) Reducing vendor delivery uncertainties in a JIT environment. J. Opns Mgmt 6(4), 381-392. 7. JacksonGC (1983) Just-in-timeproduction:Implications for logistics managers. J. Bus. Logist. 4(2), 1-19.
566
Campbell, Joshi--Materials Receiving Capacity and Inventory Management
8. Joshi K and Campbell JF (1991) Managing inventories advantages and implementation issues of just-in-time in a JIT environment. Int. J. Purchasing ~ater. Mgmt. production systems. J. Opns Mgmt 3(I), 1-11. 27(2), 32-36 14. Schonberger RJ and Gilbert JP (1983) Just-in-time 9. Karmarkar U (1989) Getting control of just-in-time, purchasing: A challenge for US industry. Calif. Mgmt Harv. Bus. Rev. 67(5), 123-131. Rev. 26(1), 54-68. 10. Lieb RC and Millen RA (1987) JIT and corporate 15. Scpehri M 0986) Just in Time, Not Just in Japan: transportation requirements. Working Paper No. 87-69, Case Studies of American Pioneers in JIT. American College of Business, Northeastern University, Boston, Production and Inventory Control Society, Falls Church, MA. VA. II. Osteryoung JS, Nosari E and McCarty DE 0986) 16. Woolsey RED 0988) A requiem for the EOQ: An Use of the EOQ model for inventory analysis. P r o d n editorial. Prodn Inventory Mgmt J. 29(1), 68-72. Inventory Mgmt J. 27(3), 39-46. 12. Plossl GW and Wight OW (1967) Production and AODmF.SSVOI~CORnESPONDF.~C~Dr JFCampbeii, School of Inventory Control. Prentice-Hall, Englewood Cliffs, NJ. BusinessAdministration, Universityof Missouri-St Louis, 13. Schonberger RJ (1982) Some observations on the 8001 Natural Bridge Rd, St Louis, MO 63121, USA.
0305-0483/91 $3.00 + 0.00 Copyright © 1991 Pergamon Press plc
Materials Receiving Capacity and Inventory Management JF CAMPBELL K JOSHI University of Missouri-St Louis, USA (Received April 1990; in revisedform February 1991) This paper analyses the optimal level of materials receiving capacity for a manufacturer that receives deliveries from many suppliers. Inventory levels and inventory carrying costs depend on the frequency of deliveries and thus, on the materials receiving capacity. An analytic model that captures the tradeoff between inventory costs and materials receiving costs is presented and discussed. The receiving cost is modeled as increasing in discrete jumps of varying sizes whenever materials receiving resources are added. Practical issues in implementing the model are highlighted and methods to reduce the marginal materials receiving cost are discussed. The paper also discusses connections to the ,liT approach for production environments where materials receiving is heavily automated.
Key words--inventory control, just-in-time, EOQ
INTRODUCTION MATERIALS management encompasses issues in a variety of areas, including inventory management, purchasing, warehousing, materials handling, transportation and customer service, Although much research has focused on inventory management decisions involving order quantities, reorder points and safety stocks, decisions involving the materials receiving process have received less attention. Determing the amount of materials handling equipment that should be installed, the number of employees that should be assigned to processing deliveries, and the nature and degree of automation in handling deliveries are important decisions for many organizations. A fundamental question for the materials receiving process is: "What should be the overall materials receiving capacity?" Although the materials receiving capacity can be viewed as fixed in the short-term, it may vary in the long-term with the addition and deletion of materials receiving resources (e.g. materials 559
handling equipment, labor, documentation and inspection capabilities and facilities, etc.). Determining the optimal materials receiving capacity helps to determine the optimal level of these resources. Increasing the receiving capacity may be expensive, but it permits more frequent deliveries, which reduces the average inventory levels and, consequently, the inventory carrying costs. This paper analyses the tradeoff between the cost of increasing the materials receiving capacity and the cost savings from reduced inventories. Items delivered to an organization can often be classified as either regularly consumed items or special items. Regularly consumed items are those common to many products, so there is generally a high demand for these items. Special items are those needed for special products and consequently have a low demand. This paper focuses on the regularly consumed items delivered to a manufacturer. In high volume mutli-product production environments, many of the items are regularly consumed items cornmort to all or most of the products. Even in job shops, many of the items, such as hardware,
560
Campbell, Joshi--Materials Receiving Capacity and Inventory Management
bearings, electrical components, etc. tend to be common to many products, The annual demand for regularly consumed items can often be estimated based on past data, so that annual orders can be placed with suppliers. Annual ordering benefits the manufacturer by providing leverage to negotiate better prices and reducing the order cost and effort. Annual ordering benefits the supplier as well, by providing large orders and advance notice, The second author's experience with a number of companies indicates that annual ordering of regularly consumed items is a common practice. Once annual orders are placed, delivery frequencies must be specified for each item. Delivery frequencies may be adjusted periodically (e.g. monthly) to better meet demand. This paper determines the optimal materials receiving capacity for regularly consumed items delivered from a number of different suppliers. This paper considers those items for which the consumption pattern and annual demand can be estimated, so that annual orders are placed, The traditional EOQ model could be used to determine an optimal delivery quantity and thus, an optimal delivery frequency, for each item separately. Summation of the individual EOQ delivery frequencies yields a total delivery frequency or capacity. However, there are some difficulties with this approach. The difficulty in accurately estimating and assigning order costs to individual items is well known [11, 16]. In purchasing environments with long term (e.g. annual) order contracts, the ordering costs are already sunk and therefore are not relevant for future delivery decisions. The incremental cost for receiving a delivery is relevant for the EOQ analysis. However, even this cost may be difficult to estimate. Another problem is that the receiving capacity provided by a set of resources may exceed the capacity that results from summing the individual item EOQ delivery frequencies. Inventory costs could then be reduced by increasing the delivery frequencies above the EOQ levels to fully utilize the available receiving capacity, An additional problem with determining a total receiving capacity by summing the individual EOQ delivery frequencies results from the implicit assumptions that the marginal cost of receiving an additional delivery is constant and that receiving capacity can always be added in small increments. These assumptions imply that the cost for receiving deliveries is a linear
function of the receiving capacity. However, materials receiving resources are often acquired in discrete units (e.g. one fork-lift or one worker). Thus, the cost for receiving deliveries is a discontinuous function of the receiving capacity that increases in discrete jumps when resources are added. This paper analyses the tradeoff between materials receiving costs and inventory costs to determine the optimal materials receiving capacity by considering the items received in aggregate, instead of separately. Neither the EOQ model nor this paper explicitly consider transportation costs. The inventory management approach suggested in this paper consists of two steps. The first step, which is to determine the optimal receiving capacity, is the subject of this paper. The second step, which is to divide the receiving capacity among the items in an optimal fashion, was addressed elsewhere [8]. The remainder of this paper is divided into five sections. The next section discusses materials receiving costs. The following section discusses the optimal total materials receiving capacity. The following section examines some practical issues and presents an example. The following section highlights the connection between the model presented in this paper and the JIT approach. The final section is a discussion of the paper and some limitations. MATERIALS RECEIVING COSTS The tasks required to receive a delivery can be divided into clerical tasks, materials handling tasks and quality assurance tasks. Each task requires certain materials receiving resources, and a given set of receiving resources provides a certain receiving capacity. For a given set of receiving resources, many of the receiving costs (e.g. salaries, equipment costs and overhead) are already sunk or committed. Therefore, these costs are largely independent of the number of deliveries. This paper addresses situations where the marginal cost of receiving an additional delivery is negligible, unless additional resources are required. Thus, the receiving cost increases in discrete amounts when resources are added. The cost and type of resources added depend on the level of receiving capacity that exists and the type of additional resources needed. Increasing the receiving capacity may involve adding
Omega, Vol. 19, No. 6
workers at relatively low cost or adding cranes or lift trucks at relatively high cost. The marginal cost to receive an additional delivery should generally be small in situations where there have been significant investments in automation and materials handling equipment and facilities. A later section discusses how the marginal receiving cost may be reduced through automation, computerization and the efficient design, organization and operation of receiving and storage areas, It is important that all three areas, clerical, materials handling and quality assurance, have the same receiving capacity for efficient operations. An area that has a much lower capacity than the others will serve as a bottleneck and limit the overall receiving capacity. Therefore, investments in each area should be based on balancing the materials receiving capacity of all areas, OPTIMAL TOTAL MATERIALS RECEIVING CAPACITY The Appendix presents a model of the inventory and materials receiving cost. The inventory cost is a decreasing function of the number of deliveries. The materials receiving cost is an increasing step function of the number of deliveries. The receiving capacity and the receiving cost increase in discrete jumps each time that receiving resources are increased. Increasing the receiving capacity allows more frequent deliveries, which lowers inventory costs, but it requires additional investments in manpower or equipmerit. The model captures the trade-off between the inventory and receiving costs to determine the optimal materials receiving capacity, This model is most applicable to organizations that receive large volumes, so that the materials receiving personnel and equipment are fully utilized for receiving and are not available for other activities. Thus, for a fixed receiving capacity, the receiving cost is fixed and the inventory cost is minimized by fully utilizing the available receiving capacity. Because the minimal total cost occurs when there is no excess receiving capacity (for a given level of investment), the optimal receiving capacity can be found by analyzing the total cost at the points which correspond to fully utilized receiving capacities. Figure 1 shows the inventory, receiving and total costs. The small steps in the receiving cost
a00 is0 160 140 120 t00 _
~ ~ ~ ~ Z s0 ca 60 ~ 40 20
o
561
u \
\
I
~
]
~
Receiving cost
_ ] ~"
I
~.......~Inventory cost
I
I
I
I
20 40 60 ao loo Number of deliveries (thousands) Fig. I. Inventory, receiving and total cost.
curve might correspond to adding workers, while the large steps could correspond to adding expensive equipment. The optimal receiving capacity can be found by analyzing the cost only at the points that are local minima of the total cost in Fig. 1. The receiving capacity that results from summing the individual delivery frequencies from separate EOQ analyses may not fully utilize this optimal receiving capacity and thus, may result in a larger total cost. PRACTICAL ISSUES The optimal delivery frequencies for each item (calculated as N~* in the Appendix) need to be adjusted based on practical considerations. The receiving capacity should generally be set to allow a safety cushion above the level of the average number of deliveries per day. Although attempts should be made to schedule deliveries to balance the workload throughout each day and week, there will likely be times when the short-term receiving capability must exceed the average. If only a fraction fl (0 < fl < l) of the receiving capacity is to be used on average, then the analysis in the appendix holds if the number of deliveries is multiplied by ft. The optimal delivery frequencies should be adjusted to sensible values that fit into natural business cycles, such as once a month (12 times per year), twice a month (24 times per year), once a week (52 times per year), twice a week (104 times per year), once a day (260 times per year), etc. Slight adjustments to the delivery frequencies should not increase the cost significantly, because of the inventory and receiving cost tradeoffs. In theoretical models, the inventory cost is halved when a given demand is delivered twice a day instead of once a day. From a practical
Campbell, Joshi--Materials Receiving Capacity and Inventory Management
562
financial standpoint, the inventory cost for an item which is received more than once a day should be no different than if that item was received only once a day, because finance charges generally apply in units of days, not fractions of days. However, transportation and storage space considerations may make a single daily delivery of bulky items undesirable. For example, delivering items with insignificant storage space requirements once per day instead of several times per day may not increase the actual (as opposed to theoretical) inventory cost. However, multiple daily deliveries may be required for bulky items for which one day's supply exceeds one delivery vehicle load. When the optimal dehvery frequencies are adjusted to account for practical considerations, additional receiving capacity may be freed up. This additional receiving capacity can then be reallocated to other items to reduce inventory costs. Adjusting delivery frequencies to practical values is illustrated in the following example, Assume that a manufacturer orders 1260 items which can be divided into 3 classes as follows: Class
i 2 3
Number of items
,4nnualexpenditure per item
IO 250
s5,ooo,ooo 75,000
1000
200
~
t so
~ ~ ~ ~ ~ o
160 140 120 too -80s0 -40 20 0
~
~
r
I
3
Deliveries/year
0.013SN 0.00170s
0.000438N
where N is the total number of deliveries received per year (to be determined), Suppose that the materials receiving cost curve is estimated by the following set of costs and capacities: Cost
Capacity
($ per year)
(deliveries/,veaQ
15,000 30,000 45,1300
9000 19,000 30,000
55,ooo 70,000 83,000 92,000
Receiving cost Inventory cost
I I I I I 20 40 60 80 100 Number of deliveries (thousands) Fig. 2. Costs for example.
The capacity values are the maximum number of deliveries per year for a given cost. Suppose that these capacity values have already been adjusted to allow a margin of safety. The inventory, materials receiving the total costs are plotted in Fig. 2 for this example. The optimal receiving capacity will occur at one of the local minima of the total cost function in Fig. 2. The optimal capacity and cost can be found graphically or by evaluating the total cost at the seven capacity values listed above. The minimum total cost is $117,129 which occurs for an annual delivery capacity of 42,000. The optimal number of deliveries per year for each class of items is then: Class
I 2
" ~
5,000
To keep the illustration simple, assume that each item in a class requires the same annual expenditure. Therefore, all the items in a particular class will have the same number of deliveries. Assume an inventory carrying charge of 20% per year. The optimal delivery frequency for each class can be computed from Equation (A4) in the Appendix: Class
.
42,00o 53,000 76,000 t0o,00o
Deliveries/)'ear
2I
579.6
3
18.4
71.4
Each of the ten items in Class 1 should be delivered approximately 580 times per year, or 2.2 times per day (assuming 260 days per year). However, it is more practical to deliver each Class 1 item two times each day, i.e. 520 times per year. Changing the delivery frequency for the 10 Class 1 items from 580 times per year to 520 times per year allows an additional 600 deliveries each year. Adjusting the delivery frequencies for Class 2 and 3 items to consume this excess capacity will reduce the total cost. The following set of adjusted delivery frequencies fit into regular business cycles and require an annual receiving capacity of 42,000. Class I 2 3
Deliveries/year 520 (two times each day) 78 (three times every two weeks) 17.3 (once every three weeks)
The deliveries should be scheduled over the weeks to balance the workload as much as possible.
Omega, Iiol. 19, No. 6
CONNECTIONS TO THE JIT APPROACH
563
Organizations that have adopted the JIT philosophy have found novel ways to reduce Just-in-time (JIT) production systems have production set-up costs, including tool re-design, revolutionized production and inventory man- faster clamping devices and work area reorganagement practices and helped many organiz- ization. Applying the same approaches and the ations to improve both productivity and quality same initiative to the receiving process could [13-15]. A fundamental tenet of JIT production result in achieving greater receiving capacities systems is to produce in small lot sizes. Major with smaller investments. Whether or not an benefits include smaller inventories (which results organization adopts the JIT approach, the marin less inventory investment and less space re- ginal cost of receiving a delivery may be reduced quired), reduced scrap and rework, less inventory by a variety of actions. The marginal cost of accounting, faster feedback on defects and higher clerical work involved in handling a delivery can quality. JIT manufacturers have tried to extend be substantially reduced through computerizthe JIT philosophy to their suppliers by encour- ation. Data input chores can be eliminated by aging suppliers to make many deliveries of small EDI (Electronic Data Interchange) or by introshipment sizes, ducing barcodes and delivery documents that can The model presented in this paper generally be read directly by optical scanners, Marginal provides a wide range of optimal delivery fre- materials handling costs can be reduced by autoquencies for different items because of the large mating materials handling and unpackaging differences in the annual consumption in dollars, and through efficient design of the unloading, In some mass production environments it may unpackaging, and inspection complex. Redesign be prudent to invest heavily in materials receiv- of packaging may reduce unpackaging costs. ing automation in view of the large volume of Marginal inspection costs can be reduced by deliveries to be received and the economies of adopting a suitable quality assurance approach scale in receiving. Automation of the receiving at the vendor. Redesign or reorganization of the process is one way to reduce the marginal receiving and storage areas may also lead to cost to receive an additional delivery. As the reduced receiving costs. marginal receiving costs are reduced, the optimal Gordon [4] describes the implementation of an receiving capacity shifts towards more frequent automated receiving system at United Stationers, deliveries, the largest wholesaler of office products in the Extensive automation of the receiving process United States. A key to implementation was generally requires large initial costs for equip- computerization of many of the receiving activiment and facilities, but reduces the marginal ties previously done manually. Prior to autocosts for receiving additional deliveries. Auto- mation, receiving was done with a log book and marion of the receiving process is advisable telephone and shipments were never received when the volume of deliveries received is large against purchase orders. After automation, supenough that the marginal cost savings with auto- pliers or carriers were instructed to call for a mation exceed the initial costs for equipment delivery appointment. Deliveries were scheduled and facilities. If the receiving capacity is very and purchase order information was made availlarge, then the delivery frequency for each item able to check against the arriving shipments. The should be increased to its maximum level in computer system even provided instructions order to minimize inventory costs. When delivery for storage locations to maximize efficiency. frequencies are very high (e.g. at least once each Bar coding was used extensively and hand-held day), then the delivery schedule will approach laser scanners and thermal label printers were that for a JIT system. The model presented in acquired for maximum flexibility. Thirteen this paper shows that lower marginal receiving major distribution centers, each averaging costs result in larger optimal receiving capacities. 250,000 square feet, were automated over a one The extreme case of the model in which marginal year period. receiving costs are negligible indicates the desirObviously, considerations and costs other than ability of a JIT receiving process. If receiving receiving play very important roles in YIT sysand transportation costs are fixed, then JIT terns. Consolidation, economies of scale, and receiving with the smallest feasible shipment size considerations of transportation and storage is optimal, space may dictate delivery frequencies for some
564
Campbell, Joshi--Materials Receiving Capacity and Inventory Management
items [1]. For example, in a television manufacturing plant, picture tubes may be delivered more than once per day, while a small washer may be delivered once every two days or once a week. The role of transportation in JIT systems has been studied from a number of perspectives [2, 6, 7, 10]. The lack ofreliable on-time delivery has been perceived as a major impediment for JIT implementation [3]. As delivery frequencies increase, transportation reliability and cost become more important and the benefits of haying suppliers located close to manufacturers are obvious. The model presented in this paper does not account for transportation costs. Thus, it is most appropriate for situations in which receiving costs are more important than transportation costs, Clearly, JIT systems are not the answer in all situations. For small and medium sized organizations that do not have a mass production environment or a large enough operation, it may not be advisable to invest heavily in receiving automation to create a very large receiving capacity. In such a case, a strict JIT approach may not be optimal. For many manufacturers, a combination of JIT and MRP ideas may govern production and purchasing [9]. The model presented here provides insights for optimizing the investment in receiving capacity to minimize the total inventory costs in these environments, DISCUSSION The management of inventories remains an important activity with significant impacts on the profitability of an organization. This paper provides useful insights into the management of inventories and the optimization of materials receiving capacity. This paper relaxes some of the assumptions employed in the EOQ model by modeling the materials receiving cost as a discontinuous function of the receiving capacity, This paper optimizes the receiving capacity by examining the tradeoff between higher receiving costs and lower inventory costs, both of which result from higher delivery frequencies. The optimal receiving capacity provides a guideline for the investment in resources required for materials handling, inspection, document processing, etc. After the optimal receiving capacity is determined, it can be allocated among the many individual items to minimize inventory costs as shown in the example,
The model presented in this paper should be useful for organizations involved in job shop or batch oriented production, where there is generally an accumulation of inventories in the warehouse. On the other hand, in high volume production environments, under a JIT program, materials may be sent directly from receiving to the production lines, thus minimizing the accumulation of inventories and materials handling. In such mass production environments, control of flow and production efficiencies may require a high level of automation and elimination of receiving bottlenecks. This model is primarily applicable to job shop and batch production environments in which the accumulation of inventories decouples the issue of receiving efficiencies and production efficiencies. A limitation of the model presented in this paper is that transportation costs have not been considered. However, the model should be applicable when marginal unit transportation costs (with respect to frequency) are much less than the marginal receiving costs (assuming the mean and variance of lead time are independent of shipment size). The model is also applicable if the transportation costs per unit weight are independent of the shipment size (i.e. the frequency of deliveries). Finally, the steps needed to implement the model for items ordered on an annual basis are summarized as follows: (1) Estimate the existing receiving capacity in terms of the number of deliveries that can be handled annually. This may be based on the number of deliveries in the previous year, an estimate of the capacity utilization and any resources added since the previous year. Also estimate the annual consumption for each item and the inventory carrying costs. (Note that it is not necessary to estimate the reorder cost.) (2) Estimate the incremental costs involved in expanding the receiving capacity by small steps (e.g. a 2% increase). Plot or tabulate the costs and the corresponding receiving capacities. (3) Compute inventory costs associated with different receiving capacities based upon equation (A5). Add the inventory
565
Omega, Vol. 19, No. 6
COSTSto the receiving costs in the graph or table from step 2.
For a constant demand rate the average inventory value for item i is Ai/(2Ni) and the average inventory cost for all k items is C~(N):
(4) Identify the optimal delivery receiving capacity from the graph or table. (5) Allocate the optimal receiving capacity to individual items according to equation (A4). Note that estimation of the receiving capacities and costs in step 2 should usually include some safety margin to handle peak loads, which exceed the average load due to the inability to achieve completely balanced delivcry schedules. The possibility of diverting resources from other areas for short periods of time to handle peak loads should be considered in arriving at the safety margin for receiving resources.
APPENDIX This Appendix presents a model of the materials receiving and inventory cost for a manufacturer that receives k items from suppliers. Assume that if there are several items sent from one supplier they are consolidated to the extent possible into an item bundle, so that the term item below may refer to a bundle of items when appropriate, The materials receiving cost to receive N deliveries per year is C o ( N ) , which can be modeled as a step-function of the form CD(N)=M/
Rj_t
j=l,2 .....
(AI)
where the Rjs are the values at which the receiving capacity and cost increase, R0 = 0 and M / > Mj_ 1. Each value of Mj is the cost to provide receiving capacity of at least R~_ I, but not more then Rj deliveries per year. Define the following in order to formulate the inventory cost: A i -- annual dollar consumption for item i;
I = inventory carrying charge (% per year); Ni = delivery frequency for item i (deliveries per year); N = total delivery frequency for all k items,
C~N) = (I/2)~A,/N,, i=1
(A2)
where k
F. Ni = ,-1
(A3)
N.
Determining the optimal delivery frequency for item i was the focus of Joshi and Campbell [8]. Optimal delivery frequencies can also be found using Lagrange multipliers (e.g. Hadley and Whitin [5]) or using the LIMIT model (e.g. Plossl and Wight [12]). The optimal delivery frequency from [8] is: (A4) k )".x/~, ,-, From equations (A2) and (A4), the minimal inventory cost with a total of N deliveries per year, C~'(N), is N* = Nx/-~
CT(N)--~-~ Z
2.
(A5)
The sum of the inventory cost and the materials receiving cost is TC(N) = C~(N) + Co(N ).
(A6)
Because the inventory cost is a decreasing function of the number of deliveries, N, and the receiving cost is piece-wise constant, the total cost achieves a local minimum for each value of Rj. Thus, the optimal cost is min{TC(R/)}. j REFERENCES
1. Ansari A and Heckel J (1987) JIT purchasing: Impact of freight and inventory costs. J. Purchasing Mater. Mgrnt 23(3), 24-28. 2. Bagchi PK (1988) Management of materials under just-in-timeinventorysystem:A new look. J. Bus. Logist. 9(2), 89-102. 3. Cheng TCE (1988) The just-in-time production: A survey of its developmentand perception in the Hone Kong electronics industy. Omega 16(1), 25-32. 4. Gordon J (1990) A manual for automation.Distribution g9(2),48-54. 5. HadleyG and WhitinTM (1963) Analysis of Inventory Systems. Prentice-Hall, EnglewoodCliffs, NJ. 6. Hill AV and Vollman TE (1986) Reducing vendor delivery uncertainties in a JIT environment. J. Opns Mgmt 6(4), 381-392. 7. JacksonGC (1983) Just-in-timeproduction:Implications for logistics managers. J. Bus. Logist. 4(2), 1-19.
566
Campbell, Joshi--Materials Receiving Capacity and Inventory Management
8. Joshi K and Campbell JF (1991) Managing inventories advantages and implementation issues of just-in-time in a JIT environment. Int. J. Purchasing ~ater. Mgmt. production systems. J. Opns Mgmt 3(I), 1-11. 27(2), 32-36 14. Schonberger RJ and Gilbert JP (1983) Just-in-time 9. Karmarkar U (1989) Getting control of just-in-time, purchasing: A challenge for US industry. Calif. Mgmt Harv. Bus. Rev. 67(5), 123-131. Rev. 26(1), 54-68. 10. Lieb RC and Millen RA (1987) JIT and corporate 15. Scpehri M 0986) Just in Time, Not Just in Japan: transportation requirements. Working Paper No. 87-69, Case Studies of American Pioneers in JIT. American College of Business, Northeastern University, Boston, Production and Inventory Control Society, Falls Church, MA. VA. II. Osteryoung JS, Nosari E and McCarty DE 0986) 16. Woolsey RED 0988) A requiem for the EOQ: An Use of the EOQ model for inventory analysis. P r o d n editorial. Prodn Inventory Mgmt J. 29(1), 68-72. Inventory Mgmt J. 27(3), 39-46. 12. Plossl GW and Wight OW (1967) Production and AODmF.SSVOI~CORnESPONDF.~C~Dr JFCampbeii, School of Inventory Control. Prentice-Hall, Englewood Cliffs, NJ. BusinessAdministration, Universityof Missouri-St Louis, 13. Schonberger RJ (1982) Some observations on the 8001 Natural Bridge Rd, St Louis, MO 63121, USA.