Semiconductor supply planning by considering transit options to take advantage of pre-productions and order cancellations

Simulation Modelling Practice and Theory 41 (2014) 46–58

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Semiconductor supply planning by considering transit options to take advantage of pre-productions and order cancellations Daisuke Yagi a,⇑, Keisuke Nagasawa a,1, Takashi Irohara a,1, Hans Ehm b,2, Geraldine Yachi b,2 a b

Department of Information and Communication Sciences, Sophia University, 7-1 Kioi-Cho, Chiyoda-Ku, Tokyo, Japan Infineon Technologies AG, Am Campeon 1-12, 85579 Neubiberg, Germany

a r t i c l e

i n f o

Article history: Received 16 June 2013 Received in revised form 4 October 2013 Accepted 12 November 2013 Available online 7 December 2013 Keywords: Semiconductor Supply planning Simulation Supply chain management

a b s t r a c t One of the objectives of supply planning is to find when and how many productions have to be started to minimize total cost. We aim to find the optimum. Base data like the length of transit time are important parameters to plan for the optimum start of production. In this research, we considered two kinds of transit options: normal transit and emergency transit, and we distinguished between planned and executed transit. The decision regarding which transit option to choose for the execution is trivial because emergency is only used when it is needed since normal transit is more cost efficient. However, for planning purpose, it is more difficult to decide which transit option should be used since the uncertainty in demand and supply between plan and execution can allow to plan an emergency transit but to execute the delivery with normal transit, which is a huge benefit in the competitive capital intensive semiconductor industry. If we planned an emergency, we can save inventory and production cost as we can delay the start of production. In contrast, we need pay additional transit cost in case that emergency transit is actually executed. Many characteristics of the semiconductor industry, which might be the front runner for many other industries, are considered in this model such as demand uncertainty, supply uncertainty and economic volatility. In our numerical experiments, we could gain the optimum, depending on each economic situation. Furthermore, we conducted sensitivity analysis of the effect of demand and supply uncertainties on total cost. Ó 2013 Elsevier B.V. All rights reserved.

1. Introduction Supply planning has played an important role for supply chain management. Supply planning role is to best match the demand on the available capacities to enable efficient production planning and order management (in resource and time). There are many methods to solve a supply planning problem such as optimization and simulation, and one of the objectives is usually to minimize the total cost associated with a release plan such as production cost, transit cost and penalty cost [24]. It is important to focus on the semiconductor industries because there are many unique characteristics in the semiconductor industry, which might be front-runner for many other industries. Thus, there are many supply chain researches which focus on semiconductor industries. One of these characteristics is that cycle time tends to be quite long because of the

⇑ Corresponding author. Tel.: +81 3 3238 3403/+81 80 5692 8482. E-mail addresses: [email protected] (D. Yagi), [email protected] (K. Nagasawa), [email protected] (T. Irohara), hans.ehm@infineon.com (H. Ehm), geraldine.yachi@infineon.com (G. Yachi). 1 Tel.: +81 3 3238 3403. 2 Tel.: +49 89 234 28480. 1569-190X/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.simpat.2013.11.007

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complexity of production [9]. Consequently, it is difficult to forecast customers’ demand accurately at the time when production starts [15], and there is a high possibility that orders are cancelled. It is also difficult to forecast production cycle time because of the complex production process [21]. Production cycle time from wafer facilities to customers is about 4 months long and production may be finished earlier or later than expected. Thus it is difficult to forecast uncertainty of the production cycle time accurately [19]. To deal with these uncertainties, it is quite important to shorten cycle time. Next, the economic volatility is also an original characteristic of semiconductor industries. This high economic volatility stems largely from the bullwhip effect [8]. When an economic situation is strong, production and transit are very busy because we have to produce and transport many items in contrast to downturn period [3]. Supply planning problem was studied by many researchers. Byrne et al. [5] used optimization to solve production and supply planning. While they did not consider demand and supply uncertainty, they could evaluate the solution of optimization by using simulation. There are also many researches about evaluation of uncertain elements, such as demand, supply and lead time uncertainties. Heydari et al. [12] researched lead-time variation impact on supply chain performance by using simulation. Acar et al. [1] studied the impact of demand and supply uncertainties in addition to lead-time variation on supply chain performance. Chong et al. [7] analyzed the impact of frequency of inventory information update, demand variability and due date variability on the semiconductor supply chain. Hung and Chang [13] aimed to determine safety stocks for production planning in uncertain production. They considered the uncertainty of flow times and yield rates as two major sources of uncertainty in semiconductor manufacturing. They formulated the simulation to solve this problem. Rastogi et al. [23] considered capacity planning for semiconductor manufacturing with uncertain demand. They formulated this problem as a stochastic mixed integer program with recourse that reduces the overall risk in planning. It is quite important to consider uncertain elements in semiconductor industry because of the existence of high variability of demand and supply. Furthermore, a lot of researchers aimed to consider these uncertainties on supply planning problems. Zhang et al. [26] considered demand uncertainty to make supply plan. They assumed that there are two kinds of demand uncertainties. One is the seasonal demand fluctuations and the other is market growth. They formalized this problem as a two-stage stochastic optimization problem. Liu et al. [18] considered both demand and supply uncertainty in production planning for semiconductor manufacturing. Manufacturing capabilities and order information from customers are random variables. They used genetic algorithm (GA) to solve optimization problem. And they used simulation when they evaluated each chromosome in GA. That is way they integrated simulation and optimization. Thus, solution of optimization was feasible and beneficial under any circumstances. Han et al. [11] studied supply planning in semiconductor industry where the quality of product is uncertain. They formulated dynamic multi-period yield management problem of a two-stage make-to-stock system with substitution faced by a semiconductor manufacturing firm. They tried to determine the optimum production input quantity in order to maximise the firm’s profit. Ponsignon and Mönch [22] solved master planning problems that arise in semiconductor industry. They formulated this problem as a mixed-integer programming (MIP) model, and proposed heuristic procedures to solve the problem efficiently. However, they did not consider uncertainty such as demand variability, and they assumed a fixed production lead time. Leachman and Ding [17] solved the manufacturing management problem which integrated the speed economics. The prices of semiconductors decline very quickly compared with other industries. And they concluded the value of manufacturing speed is substantial in the semiconductor industry. It is useful to set up multi transit options to save the supply planning cost. If there are multi transit options, we can choose the transit option flexibility in accordance with the production cycle. However, there are not so much researches which considered transit options in supply chain design and management. The earliest model with emergency transit may be built by Barankin [4]. In this paper, a single period model was developed in which a shipment is received at the beginning of the period and an emergency order is placed at some time during the period. Khouja [14] determined the profit maximising order quantity for a single period model with an emergency supply option, and showed that this quantity is smaller than the solution of the newsvendor model. Pishvaee and Rabbani [20] considered two kinds of transit options: via Distribution Center (DC) and directly to customers. They solved this problem as facility location problem. The objective is to minimize total cost including fixed opening costs, processing and transportation costs and penalty costs. They decided where factories and DC have to be built and how many items are transported. However, they did not consider any uncertain elements. In this study, graph theoretic approach is used to escape from the complexity of mixed integer mathematical programming models. Chan and Zhang [6] considered the impact of the length of transportation lead time on supply chain performance. They built the simulation model, and conducted sensitive analysis on supply chain cost: holding cost, penalty cost and ordering cost. Their results revealed that flexibility of transportation could reduce the retailer’s total cost and improve its service level. There is no research that integrates transit options into supply planning problem. Consequently, the uniqueness of this research is that we consider transit options in the semiconductor supply planning problem. In addition, we consider demand uncertainty, supply uncertainty and economic volatility to make this research practical.

2. Proposed model 2.1. Problem outline In this research, we aim to make a supply plan that minimizes the total cost. Fig. 1 depicts the supply chains which were used in this research. Products are produced at the factory. Normally, products are sent to a Distribution Center (DC) and

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Normal transit DC

Factory

Customer

Emergency transit Fig. 1. Supply chain.

stocked. If there is a demand from the customer, stocks are sent to the customer from DC. However, sometimes, in an emergency situation, the factory has to send items directly from the factory to the customer in an emergency situation. These two transit options are called normal transit and emergency transit respectively. To solve this problem, we used simulation model which simulates the supply plan, the actual production and the actual transit. Simulation is effective for semiconductor manufacturing because the situation is different between the time when plan is made and when production and transit is actually executed [10]. First, we explain parameters of the simulation: order information, order cancellation, pre-production and economic volatility. Second, we show the decision variables (output) of the simulation: normal transit and emergency transit. Lastly, we provide the explanation of the evaluation criteria: total cost. For the convenience, the following assumptions are adopted in the study. Assumption 1. The supply planning is performed on weekly granularity. Assumption 2. There is one kind of item. Before we explain each component, we provide the explanations for indices, parameters and variables which are used in this model. Indices i 2 I ¼ f1; 2; ldots; ng: Index of order w 2 W ¼ f1; 2; . . . ; mg: Index of planning horizon (week) Parameters cn(1): Cost for normal transit from factory to DC cn(2): Cost for normal transit from DC to customer ce: Cost for emergency transit from factory to customer tn: Length of transit time for normal transit from factory to customer (day) te: Length of transit time for emergency transit from factory to customer (day) s: Saving cost of emergency transit plan Ri: Reception week for order i Di: Due week for order i c: Base order cancellation rate (1 week before due week) Ci: Cumulative order cancellation rate for order i Lm: Mean of the lead time Lsd: Standard deviation of the lead time pm: Mean of pre-production days in downturn psd: Standard deviation of pre-production days in downturn Pm: Mean of pre-production days in each economic situation Psd: Standard deviation of pre-production days in each economic situation E: Limit of the number of emergency transit e: The number of emergency transit which was already used v: Indication of economic situation from downturn to upturn [0, 1] B: Border week to decide the supply plan Sw: The number of stock at DC in the week w rci : Uniform random variables U[0, 1] for order cancellation for order i rli : Normal random variables N(Lm, Lsd2) of the lead time for order i

rpi : Normal random variables N(Pm, Psd2) of pre-production days for order i

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Decision variables  1 : Order i is planned as emergency transit plan: xi ¼ 0 : Order i is planned as normal transit plan:  1 : Order i is transported as emergency transit from factory to customer: yi ¼ 0 : Order i is not transported as emergency transit from factory to customer:  1 : Order i is transported as normal transit from factory to DC: ð1Þ zi ¼ 0 : Order i is not transported as normal transit from factory to DC:  1 : Order i is transported as normal transit from DC to customer: ð1Þ zi ¼ 0 : Order i is not transported as normal transit from DC to customer: 2.2. Parameters 2.2.1. Order information Demand information from customers, called ‘order’, is presented in an order table which provides information of reception week and due week. Each order has only one item. Order table is provided in Table 1. Reception week indicates the week when orders came from customers. Due week is the week when products have to be sent to customers. Both data are provided by customers. Lead time r li is defined as:

rli ¼ Di  Ri :

ð1Þ

We assume that lead time is a random variable; some orders have short lead time, and others are long in accordance with customers demand. 2.2.2. Order cancellation In this model, we consider two kinds of uncertain elements, demand uncertainty and supply uncertainty. First, we assume that there are order cancellations from customers as demand uncertainty. In semiconductor industries, customers tend to place more orders than the required number of products. Because the production lead time to deliver products to customers is quite long, and customers want to have an upside flexibility in case they need more products on short notice, customers tend to order products more than they actually need. Thus, we consider order cancellations as demand uncertainty. Order adding is also considered as a short order since we consider only reception week and due week as order information in this model. It is also usual that order cancellation rate becomes high as time axis approaches to the due week because customers can forecast their demand more accurately just before the due week. Therefore, we assume that order cancellation rate is given following Table 2. After we decided the base order cancellation rate c as the cancel rate when there is one week to the due week, we could calculate order cancellation rate on other weeks. In this model, we assume that order cancellation rate becomes half with the increase of the number of week to the due week. This assumption is based on simplified data from the real semiconductor company. After we define order cancellation rate in each week, it is easy to calculate cumulative order cancellation rate for order i. How to calculate cumulative order cancellation rate for order i is provided as:

(

 rl ) 1 i : C i ¼ 2c 1  2

ð2Þ

To understand easily, we would like to show one example. We use base order cancellation rate c = 0.1. If the order comes 4 weeks before the due week, then cumulative order cancellation rate for this order is 0.1 + 0.05 + 0.025 + 0.0125 = 0.1875 (18.75%). You can also use Eq. (2) to calculate cumulative order cancellation rate. There are also other ways to calculate the order cancellation rate. For example, So and Zheng [16] assume that the supplier’s replenishment lead time can affect the variability of the retailer’s order quantities. But we used the assumption based on empirical data of the semiconductor company because we focus on the semiconductor industry in this research. 2.2.3. Pre-production We consider pre-productions as supply uncertainty. Pre-production indicates that production is finished earlier than the planned date. Since the supply plan needs to be conservative to avoid delay and inability to deliver products, production have to be planned to be finished a few days earlier than the due date in semiconductor industries. In this model, the value

Table 1 Order table. Order no.

Reception week

Due week

1 .. . n

R1 ... Rn

D1 ... Dn

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Table 2 Order cancellation rate in each week. The number of week to due week

Order cancellation rate

1

2

...

w

c

c/21

...

c/2(wr)

of pre-production indicates how many days production were finished earlier than expected. We assume that pre-production days are based on normal distribution. There are two parameters to explain pre-production characteristics: mean pm and standard deviation psd. If this value is smaller than 0, this means production finished later than expected (backlog). In this case, we have to use emergency to meet customers’ demand in time. These two values pm and psd explain the value of preproduction in the downturn economic situation. Pre-productions are dependent on an economic situation. When an economy is strong, products tend not to be pre-produced because we have to produce many items in a strong economic situation, and production may not be conducted smoothly. Detail explanation for the relationship between pre-productions and economic situations is provided in Section 2.2.4. 2.2.4. Economic volatility Economic volatility is considered in this model because semiconductor industry has high economic volatility compared with other industries. We consider the optimum in each economic situation from downturn (weak) to upturn (strong). There are two effects which stem from the economic volatility. First, transit capacity is affected by the economic volatility. When an economy is in upturn, emergency transits were already used and we cannot use additional emergency transit at that time. In this model, the economic situation is defined by the indication of economic situation v. v range from 0 to 1. If v is large (1), this indicates that economy is strong. On the contrary, if v is small (0), this indicates that economy is weak. The limit of emergency transit is denoted as E, and the number of emergency transits which were already used is denoted as e. The value of e is calculated as:

e ¼ v E:

ð3Þ

If an economy is strong, many emergency transits were already used, and the limit of the number of emergency transit is small. In contrast, if an economy is weak, then few emergency transits were already used, and the limit of the number of emergency transits is large. A constraint of the number of emergency transits in each economic situation is provided as: n X yi 6 E  e ¼ Eð1  VÞ:

ð4Þ

i

Second, production capacity is also affected by an economic situation. When an economy is strong, factory cannot produce items smoothly. Consequently, the number of days of pre-productions in upturn is smaller than that in downturn. The relationship between the economic situation and pre-productions is as follows:

Pm ¼ pm ð1  v Þ þ v ; Psd ¼

fpm ð1  v Þ þ v gpsd pm

ð5Þ ð6Þ

Both the mean and the standard deviation are affected by the economic situation. Eq. (5) was constructed based on the data from the real semiconductor company. These two equations were gained by analyzing the actual data from the semiconductor companies statistically. While the mean of pre-production is 1 day in upturn, it is equal to pm in downturn. We also assume that the reliability of production is not changed in each economic situation. In other words, the ratio of the mean to the standard deviation is constant, and the possibility that the value of pre-production becomes minus (backlog) is constant. This assumption is also based on the empirical data from the real company, and expressed as Eq. (6). 2.3. Decision variables We consider two kinds of transit options in this model: normal transit and emergency transit. Through the simulation, we aim to output the supply plan as decision variables. This supply plan decides which orders have to be planned by normal or emergency transit. In this section, the explanation for these two transit options is provided. There are two characteristics to explain each transit option: the length of transit time and the cost for transit. We assume that transit time for normal is longer than that for emergency although cost for normal is cheaper than that for emergency. We distinguish transit options between plan and execution. The execution of transit might be different from the planned one since there are uncertainty in demand, supply and economic volatility. We also provide the detail explanation for the case that the execution is different from the plan.

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2.3.1. Normal transit plan If we choose the normal transit plan, we need to start the production expecting to send items by normal transit. Fig. 2(a) depicts the image of the normal transit plan. After production was finished, products are sent to customers by normal transit. However, if production were delayed because of some problems such as a strong economy, we need to use emergency transit for these orders to meet customers’ demand in time. 2.3.2. Emergency transit plan If we use the emergency transit plan, we have to start the production expecting to send products by emergency transit. That is to say we can delay the start of the production compared with the normal case. As a result, we can forecast customers’ demand more accurately. In addition, we can produce items at a lower cost because production cost is decreasing as time passes based on Moore’s law [2] and more than Moore [25]: a rapid exponential increase in the performance of chips over time. For these reasons, we can save cost for inventories and production when we use emergency transit plan because of the delay of the start of the production. The amount of cost saving from shortening cycle time is about 0.1% of cost of sales per day because we understand Moore’s Law as getting every three years the double number of transistors for the same price which means 30% cost reduction/year which is approximately 0.1% reduction per day. In this research, cost saving is denoted as s. The disadvantage of emergency transit is that we have to pay high transit cost compared with normal transit. Fig. 2(b) provides the image of emergency transit. There are three cases when the actual execution of transit is different from the planned one. First, when we planned emergency and enough pre-productions occurred in the production processes, then we can send products to customers in time by normal transit instead of emergency transit. In this case, we can use normal transit and save high transit cost for emergency. This case is explained in Fig 3. Second, when there are order cancellations from customers, we do not need to send items by emergency transit. Instead, we can send products to DC as a stock by normal transit and we can save cost for emergency transit. These inventories are used in the next case. Third, even if there is neither order cancellation nor pre-production, if there are any stocks at DC, then we can send items from DC to customers by normal instead of emergency. And the produced item at factory will sent to DC as another stock. Consequently, if these three cases occurred, we can save high cost for emergency transit and we can also gain the cost saving from emergency transit plan due to the delay of the start of production. This leads to a huge benefit in a competitive capital intensive semiconductor industry. 2.4. Evaluation criteria The objective of this model is to find the supply plan that minimizes the total cost with a release of the plan. To achieve this goal, we have to calculate the total cost as the evaluation criteria for the supply plan. In this model, we consider two kinds of cost components: the transit cost and the cost saving for the delay of the start of production because of the emerð1Þ ð2Þ gency transit plan. We define four kinds of variables to calculate total cost: xi, yi, zi and zi . We define xi to make the supply plan. How to define the value of this variable in the simulation is explained in Section 3.1. If xi = 0, this indicates order i is planned by normal transit plan. In contrast, if xi = 1, this order is planned by emergency tranð1Þ ð2Þ sit plan. Next, yi, zi and zi are variables which represent what kind of transit option was actually executed. After we simulated the actual production and transit, we can output these variables. For instance, when order cancellations occurred, these orders are transported up to DC by normal transit even if orders are planned by emergency transit. The detailed explað1Þ ð2Þ nation for how to simulate and calculate output variables yi, zi and zi is explained in Section 3.2. Finally, the calculation of total cost is provided as:

TC ¼

n n n n X X X X ð1Þ ð2Þ yi c e þ zi cnð1Þ þ zi cnð2Þ  xi s: i

i

i

ð7Þ

i

Finish production

Start production

Due week

Time axis

(a)

Normal transit plan

Production

Normal transit

Start production

(b)

Emergency transit plan

We can delay production.

Finish production Production

Saving inventory and production cost Fig. 2. Normal transit plan and emergency transit plan.

Emergencytransit

High transit cost

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Fig. 3. Changing the transit option due to the pre-production.

The first term represents the transit cost for emergency transit. The second and third terms indicate the transit cost for normal transit. Lastly, the fourth term represents the cost saving which stems from emergency transit plan. Consequently, the total cost is provided as the sum transit cost minus cost saving for emergency transit plan. If backlogs occur (the pre-production value is less than 0), then we have to execute emergency to send products to customers in time. The consideration of penalty cost can be neglected because the current reality and the new model have the same amount of penalty costs. Consequently, we do not consider any penalty cost in this model. This calculation is based on real data from the semiconductor companies. 3. Simulation model We developed a simulation model for making the supply plan and simulating actual production and transit. In this section, the detail explanation for the simulation model is provided. First, we explain how to simulate planning. And next, we show the detail explanation for the simulation of actual production and transit. Lastly, we summarize whole simulation model. 3.1. Simulation of planning First of all, orders from customers are generated in the simulation model. Each order has information of the reception week and the due week. Based on the information from customers, we need to make the supply plan: when we should start production and how to transit products. To decide the supply plan in the simulation model, we focus on the length of lead time from the reception week to the due week. If the length of lead time is long, these orders have high possibility to be cancelled because customers cannot forecast their own demand accurately when they put an order. By contrast, if the length of lead time is short, the cumulative order cancellation rate for these orders become low. Then, we set up one parameter which is used to decide the supply plan. This is border week B. When customers ordered, if the length of lead time is larger than or equal to the border week B, then these orders are planned by emergency. In contrast, if the length of lead time is smaller than the border week B, then orders are planned by normal transit. An example of border week B is shown in Fig. 4. The reason why we defined the border week B as above stated is that the emergency transit plan is beneficial if there are many order cancellations. And the cumulative order cancellation rate becomes high if the length of lead time is long. Thus, we plan emergency when the length of lead time is long enough. In contrast, we plan normal transit when it is short. Next, we show the explanation of how to simulate making the supply plan. Eq. (8) explains how to decide the supply plan xi based on the value of the border week B. Once the border week is defined, the supply plan is made based on the border week defined in step 1. This simple step is reiterated for all orders, and the supply plan is made.

Fig. 4. An example of border week B = 10.

D. Yagi et al. / Simulation Modelling Practice and Theory 41 (2014) 46–58

 xi ¼

0 if B P Di  Ri 1 if B < Di  Ri

53

ð8Þ

3.2. Simulation of actual production and transit Once the supply plan is defined, we have to simulate actual production and transit in the next step. The simulation process is different based on the plan of the transit option: normal transit plan or emergency transit plan. We explain how to simulate actual production and transit using the flow chart. The actual transit option may be different from the planned transit option because there may be some uncertain elements: order cancellations and pre-productions. 3.2.1. For normal transit plan When orders are planned by normal transit, production is started earlier than the emergency transit plan. Thus, there are only very few cases for which we have to execute the emergency. Fig. 5 shows the flow chart of actual production and transit. First, the number of products in stock at the DC is confirmed. If stocks will be available at DC on the reception week, we will send this stock from the DC to the customer by the normal transit, and we do not start production. In contrast, if no stock will be available at the DC when the order is due for shipment to customer, then we start production. Second, while we produced the item, we check whether there is the order cancellation from the customer or not. In this simulation model, we compare the random variable r ci with the cumulative order cancellation rate Ci to confirm whether an order cancellation occurred or not. When rci is smaller than or equal to Ci, the order cancellation occurred. On the contrary, when rci is larger than Ci, the order cancellation did not occur. If the order is cancelled, production is continued, and products are sent to the DC as the stock from the factory by the normal transit. If there is no order cancellation, the simulation moves onto the next step. Third, we confirm whether a pre-production occurred in the process of production or not. If the value of pre-production is positive, this shows that production is finished earlier than expected. In this case, we can use the normal to send the product to the customer because the plan is the normal transit plan. On the contrary, when no pre-production occurred, we lastly confirm the stock at the DC again. If there are some stocks at the DC, we can send this stock instead. However, if there is no stock, then we have to send products to customers by emergency to satisfy customers’ demand in time. 3.2.2. For emergency transit plan When orders are planned by emergency transit, enough amounts of pre-productions are needed to execute the delivery with a normal transit instead of an emergency. Otherwise, order cancellations or stocks at DC are needed to avoid using emergency. In this section, we provide the explanation for the simulation of actual production and transit for orders whose plan is an emergency transit. Fig. 5 also shows the flow chart of actual production and transit for emergency transit plan. The difference from previous explanation is the third step: pre-production. After production was finished, we checked whether enough pre-productions occurred or not. And if the value of pre-production is larger than or equal to the difference

Fig. 5. Flow chart of actual production and transit for order i.

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between tn and te, the normal transit option can be used instead of the emergency transit option. However, if there are no enough pre-productions, we may have to execute the emergency to send the product to the customer after confirming stock at DC. It is easily understood by seeing Fig. 3. To use a normal transit, productions have to be finished earlier than planned to satisfy customers’ demand in time. The rest of the process remains the same as the last explanation on Section 3.2.1. 3.3. Whole simulation model Lastly, we summarize the whole simulation model. Fig. 6 provides the flow chart of the whole simulation model. After we define the border week, we decide the supply plan based on the Eq. (8). After we decided the supply plan, actual production and transit are simulated based on the flow chart Fig. 5. These processes are reiterated for all orders from the customer. After we finish the simulation of production and transit for all orders, we confirm whether output solutions satisfy the constraint (4) or not. Constrain (4) indicates the constraint of the number of emergency transits. If solutions do not satisfy constraint (4), then we cannot use this supply plan. Thus we remove this supply plan from candidate solutions, and go back to Loop 2 to find the other optimum solutions for given the particular border week. Lastly, we confirm whether we conducted the simulation for all border weeks or not. If we have not finished simulation for all border weeks, we change the value of the border week and simulate planning, production and transit again. Conversely, if we finish simulation for all border weeks, we finish this simulation model. In the numerical experiments, we iterated this simulation for each economic situation. If the economic situation is different, then there are influences on production and transit. For example, when an economy is strong, pre-productions tend to be less, and there is a strong constraint for the number of emergency transits. Consequently, if we changed the economic situation, some parameters and situations are subject to be changed. Thus, the reiteration of the simulation is needed to simulate planning, production and transit in each economic situation. 4. Numerical experiments 4.1. Sensitivity analysis This experiment is conducted for confirming the effect of order cancellations and pre-productions on the total cost. First, we show the values of parameters which were used in the experiments. Table 3 shows each value of the parameters. We assume that the length of lead time is based on a normal distribution, and that mean and standard deviation is provided.

Fig. 6. Flow chart of the whole simulation model.

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This experiment was conducted in the same economic situation. Thus, we used fixed value of v for all simulations to fix the economic situation. These values of parameters in Table 3 are reliable because these were actual data provided by the semiconductor company. We conducted two kinds of sensitivity analyses. First, we confirmed how order cancellations affect the total cost. We used following values of pre-production: Pm = 3, Psd = 1.5. We calculated the total cost in each case, and also we reiterated simulations after we changed value of order cancellation rate. The result of experiment is provided in Fig 7. When border week is equal to 1, this indicates that all orders are planned by emergency transit. In contrast, when border week is 27, this indicates that all orders are planned by normal transit. From this result, we could observe that when order cancellation rate is high, emergency transit plan is beneficial. The reason is that we can send products by normal transit instead of emergency transit when there are many order cancellations. In addition, we can have enough available stocks at DC to deal with uncertain customers’ demand. While the cost-minimized border week for c = 0.050 is 12, the cost-minimized border week for c = 0.100 is 5. This cost-minimized point indicates that we can use the emergency transit plan beneficially. This means that we use the emergency transit plan although items are sent by the normal transit in fact. The right area of the cost-minimized point indicates that we can use emergency transit plan more beneficially, and the left area indicates that we used the emergency transit actually and have to pay high transit cost. From the result, when order cancellation rate is high, we should use the small value of border week. That is to say we should use emergency transit plan for many orders if there are many order cancellations. Next, we analyzed how the values of pre-production affect the total cost. We used the following order cancellation rate: c = 0.100. The result is provided in Fig 8. We could see that when the mean of pre-production is large, emergency transit plan is beneficial. The reason is that we can use normal transit instead of emergency transit if there are many pre-productions. While the cost-minimized border week for Pm = 2.0 is 19, the cost-minimized border week for Pm = 3.0 is 12. Thus, when there are many pre-productions, we should use the small value of border week. In other words, we should use emergency transit plan for many orders if there are many pre-productions. We also conducted simulations by using other parameters, such as lead time and transit cost. And the results were same as our expectation. When the lead time is very long, emergency transit plan is much more used since the order cancellation rate becomes higher and the emergency transit plan tends to be used beneficially. Furthermore, even if we change the value of the cost for transit, it did not affect the decision of the transit plan for the given border week because we decide the transit plan by the length of lead time between the reception week and the due week in the simulation. 4.2. Optimum in each economic situation We solved the supply planning problem by using a simulation model, and found optimum in each economic situation. First, we show the values of parameters which is used in the experiments. We also used the values of parameters which were shown on Table 3. We used following values of pre-production: pm = 5.0, psd = 2.5. The indication of economic situation v was changed in relation to the economic situation. For example, when v is large, this indicates the upturn situation. As I explained, production and transit are affected by the economic situation. Table 4 provides the pre-production values in each economic situation. These values are calculated using Eqs. (5) and (6). We used following three order cancellation rates to analyze the effect of order cancellation rate on the optimum: {c = 0.05, c = 0.10, c = 0.15}. We iterated simulation of planning, production and transit in each economic situation. After simulation was finished, we found the cost minimized border week which satisfied the constraint for emergency transit (4) as the optimum. Fig. 9 provides the results of optimum and Fig. 10 provides the results of the minimized total cost in each economic situation respectively. When the economy is in downturn (v is small), emergency transit plan is beneficial. Because there are many pre-productions in downturn, we can actually use normal transit instead of emergency transit. On the contrary, when the economy is in upturn (v is large), we should use normal transit to avoid risks. Since there are few pre-productions in upturn, it is too risky to use emergency transit plan. If we used emergency transit plan in upturn, we have to execute emergency and pay additional cost for emergency. Consequently, we must use normal transit plan in upturn to mitigate such risks. In addition, we could observe that the optimum became conservative when order cancellation rate is low. For example, when order cancellation rate c = 0.10, the optimum in the economic situation v = 0.6 is 8. In contrast, when c = 0.05, the optimum in the same situation is 13. Consequently, we could see that normal transit plan is often used when order cancellation

Table 3 Values of parameters. Parameter n

c ce tn te

Value

Parameter

Value

0.05 0.25 4 2

S Lm Lsd v E

0.005 10 5 0.0 1000

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D. Yagi et al. / Simulation Modelling Practice and Theory 41 (2014) 46–58

4000

c=0.000 c=0.025 c=0.050 c=0.075 c=0.100 c=0.125

3500

Total cost

3000 2500 2000 1500 1000 1

6

11

16

21

26

Border week: B Fig. 7. Sensitivity analysis for order cancellations.

6000

P m =1.0 P m =1.5 P m =2.0 P m =2.5 P m =3.0 P m =3.5 P m =4.0

Total cost

5000 4000 3000 2000 1000 1

6

11

16

21

26

Border week: B Fig. 8. Sensitivity analysis for pre-productions.

Table 4 Values of pre-productions in each economic situation. Indication of economic volatility: 0.25

0.50

0.75

1.00

0 5.0 2.5

250 4.0 2.0

500 3.0 1.5

750 2.0 1.0

1000 1.0 0.5

19

c=0.05 c=0.05

17

c=0.10 c=0.10

15

Border week: B

E Pm Psd

v

0.00

c=0.15 c=0.15

13 11 9 7 5 3 1 0

0.2

0.4

0.6

0.8

The indication of economic volatility: v Fig. 9. The optimum in each economic situation.

1

D. Yagi et al. / Simulation Modelling Practice and Theory 41 (2014) 46–58

1800

3 c=0.05

1700

2c=0.10 1c=0.15

1600

Total cost: TC

57

1500 1400 1300 1200 1100 1000 0

0.2

0.4

0.6

0.8

1

The indication of economic volatility: v Fig. 10. The minimized total cost in each economic situation.

rate is low. When there are few order cancellations, there are few available stocks at DC. Thus, we do not have to use emergency transit plan to reduce the case that we execute emergency. As a result, the supply plan became conservative when order cancellation rate is low. By contrast, we could see that the supply plan was aggressive when order cancellation rate is high. For instance, when order cancellation rate is 0.15, the optimum in the economic situation v = 0.6 is 1. Thus, emergency transit plan is often used when order cancellation rate is high. If there are many order cancellations, we can use emergency transit instead of normal transit because there are enough stock available at DC. As a result, the risk is not so high even if we use emergency transit plan for many orders. And thus, the optimum became aggressive when order cancellation rate is high. We could observe that the total cost is minimized when the emergency transit plan was most beneficially used. This means the point that the optimum border week is 1 in Fig. 9. In other words, we used the emergency transit plan a lot but we sent items by the normal transit in fact because of the occurrence of order cancellations and pre-productions. 5. Conclusion We investigated a supply planning problem considering transit options, demand and supply uncertainty, and economic volatility by using simulation. We considered two kinds of supply plan in this model: normal transit plan and emergency transit plan. Through simulation, we proposed which orders have to be planned by normal transit plan or emergency transit plan. We could gain results that indicate that using emergency transit for planning is beneficial if there are high order cancellation rate and/or pre-productions. If there are many order cancellations, we have enough stocks available at DC to send the products to customers by normal transit instead of emergency transit. In contrast, if there are low order cancellation rate, we should use normal transit plan to reduce the risk to pay high transit cost due to emergency transit. In addition, numerical experiments show that enough pre-productions make planning with emergency transit beneficial. When there are many pre-productions, there is enough time to send items to customers in time by normal transit instead of emergency transit. Thus, we gain cost saving from emergency transit plan by using emergency transit only in this situation where it is needed. On the contrary, when there are few pre-productions, emergency transit plan do not have to be used. If we planned with emergency transit, we had to send products by emergency transit, and thus, we had to pay high transit cost. In conclusion, emergency transit plan are beneficially when there are enough order cancellations and/or pre-productions. Next, we could understand the optimum in each economic situation. When the economic situation is strong, the number of pre-productions is small and we can use only a small number of additional emergency transits as the maximum amount of emergency transit is already required by the strong business situation. Thus, normal transit plan is better in upturn. In contrast, when the economic situation is weak, there are many pre-productions, and we have capacity for additional emergency transits. Consequently, emergency transit plan is more beneficial in downturn. Furthermore, we could confirm that if order cancellation rate is low, the supply plan become more conservative to reduce the risk to pay high cost. In contrast, when order cancellation rate is high, the supply plan become more aggressive because we can send items by normal transit even if the plan was to deliver with emergency transit due to order cancellations. Now, we did not consider production cost, inventory cost and backlog cost in detail. To consider these costs, it is important to apply the new method such as simulation optimization. Thanks to new method, we will be able to find optimum that minimize whole cost. In addition, we now assume that this model is applied to semiconductor industries. To apply this research to other industries, we need to interview and understand other kinds of supply chains. This will make this research more practical because the model will be able to be applied to many cases. Furthermore, we have to consider the detail of demand to make this research more practical in the future. For example, customer specific elements, such as order quantity and order item, are important to apply this research into the real world. It also makes our research more practical to consider

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multi kinds of items. To consider multi items, it is needed to budget/resource capacity and product substitution. Each product’s demand pattern should be researched to make the better plan for producers and customers. For example, the demand information is forecasted by product price, marketing effort and product inventory. While we have to improve this model in the future, we could gain practical results because we built the simulation based on actual semiconductor companies’ data and we used actual data from these companies. I hope that this research will be useful to make beneficial supply plans for industries. References [1] Y. Acar, S. Kadipasaoglu, P. Schipperijn, A decision support framework for global supply chain modelling: an assessment of the impact of demand, supply and lead-time uncertainties on performance, International Journal of Production Research 48 (11) (2010) 3245–3268. [2] A. Aizcorbe, S. 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