- Title: Value of Upstream Information in a Two-Stage Supply Chain with Random

Transcription

1 - Abstract Number: Title: Value of Upstream Information in a Two-Stage Supply Chain with Random Yields - Name of the Conference: Second World Conference on POM and 15 th Annual POM Conference, Cancun, Mexico, April 30 May 3,

2 Abstract New developments in corporate information technology such as ERP systems have allowed a lot of information to flow among members of supply chains. However the benefits of sharing information can vary depending on the supply chain structure and its operational characteristics. Most of the existing research has studied the impact of downstream (e.g. retailer to supplier) information on the performance of the supply chain. We evaluate benefits of upstream (i.e. from supplier to retailer) information sharing, in a two-stage serial supply chain in which the supplier is faced with uncertainty in yield. We are interested in determining when this upstream information is most beneficial to the retailer. After establishing the appropriateness of simple order-up-to policies, we performed a detailed computational study. We observed that information is most beneficial when there are low variations in end-customer demand, high variations in supplier s yield, and high penalty to holding cost ratio at the retailer. 2

3 Introduction We are living in the information age. The availability of information has been increasing at an exponential rate during the last decade. The explosion of information availability has given decision makers of supply chain management a lot of possibilities and opportunities for improvements in their supply chain efficiency. As knowledge is power, information is power in supply chains. It provides the decision maker the power to get ahead of the competition, the power to run a business smoothly and efficiently, and the power to succeed in an ever more complex environment. Information plays a key role in the management of supply chain. (Nahmias, 2001) Having said that about the importance of information to supply chains and abundance of it, the performance of a supply chain depends critically on how its members coordinate their decisions. It is hard to imagine coordination without sharing the information available to each member. There are a number of new emerging technologies available to connect the members of a supply chain to support information sharing. Recent development in corporate information technology such as ERP systems allows information to share seamlessly among members of supply chains. However, benefits of sharing information among supply chain members are not always the same. 3

4 It depends on the supply chain structure (e.g. serial or distributive systems) and its operational characteristics (e.g. costs involved and demand patterns). We study a serial multi-stage supply chain where holding and penalty costs are involved when faced with randomly distributed endcustomer demand patterns. Information flow can occur in two ways. One is by sharing downstream information and the other upstream information. According to Chen (2004), while a significant part of the literature is interested in the value of sharing information of the downstream part of the supply chain (i.e. the part that is closer to the end customers), upstream information (supply-side information) has received much less attention in the literature. This paper studies the value of sharing upstream information with downstream members of a supply chain. Often in supply chains, receiving quantities from supplier to retailer can be uncertain. It is called random yield problem. We are particularly interested in a case when shipping amounts from the supplier are randomly less than the ordered quantities. Some of the well-known examples of random-yield models are electronic fabrication and assembly, chemical processes, and procurement from suppliers that produce defective products (Yano and Lee, 1995). The problem of dealing with random yield is motivated by a supply chain management problem 4

5 found at a chip tester manufacturer (Gavirneni, 2003) where the makers of computer chips who supply in a serial chain to the chip tester manufacturer has significant yield losses (30-50%) in their supply chain. Yield loss problem is one of the ubiquitous problems in semiconductor manufacturing industry. In the following section, we setup two models for cost comparisons to see benefits of sharing upstream information with random yields. Then we describe the detailed simulation settings to observe in what operational characteristics the benefits are the most. After the discussion of results, we end this paper with where we are going further as future extensions. Model Setup Based on the example supply chain used by Gavirneni (2003), we set up two serial supply chain models with two stages as in Figure 1. In this setting, the supplier has two serial independent internal processes to go through for its final products. In Model 1, no upstream (supplier s) information about realized output amounts of its internal processes is shared with downstream member (retailer) of the supply chain, whereas, in Model 2, both outputs of Process 1 and Process 2 of the supplier are shared in real time with the retailer. We call Model 1 NIS (No Information Sharing) model and Model 2 ISM (Information Sharing Model) from here on. 5

6 Notations that are used in the Figure 1 are listed following the figure. Model 1 No Information Sharing (NIS) Supplier Process 1 (y 1 )? Process 2 (y 2 )? Retailer Demand (d t ) o t Model 2 Information Shareing Model (ISM) Supplier Process 1 (y 1 ) o t Process 2 (y 2 ) o t Retailer Demand (d t ) o t Figure 1. Two models of two-stage supply chains with random yields: NIS (Model 1) vs. ISM (Model 2). Notations: d t = Demand at time t i t = On-hand inventory 6

7 o t = Order placed at time t o = Realized production output of ot from process 1. t o t = Realized production output of o t from process 2. y = Order-up-to level y i = Random production yield for process i y t = Average production yield for process i For the model settings in Figure 1, when retailer places an order, supplier has to go through two processes to satisfy the order. In each process, there is an independent random yield associated with it. Output of Process 1 is randomly less than the amount retailer ordered due to defects and other causes. In the same way, output of Process 2 is randomly less than the amount it is fed from Process 1. Proportional random yield rate, one of the simplest forms of modeling random yield, is used for our models. The random yield factors are denoted by y 1 and y 2 with the averages of y1 and y 2. In order to understand the decision associated with order quantities, we need to clarify the sequence of the events that is used in our simulations in the following section. The sequence of events in terms of the retailer is as follows: 7

8 - Retailer estimates the order quantity and places an order, - Receives shipment from the supplier, - Satisfies demand, and - Pays holding or penalty costs according to the ending inventory. Given the sequence of events, the retailer has to deal with the system lead time of three periods because retailer is facing with three periods of demand uncertainty when planning for an order. One period of uncertainty is from the period when retailer places an order, and the other two are from the supplier s two processes that the order has to go though. In NIS model, retailer decides an order quantity to meet the demand in the three periods ahead based on the expected quantity of shipment in that period without knowing neither realized output from Process 1 or Process 2 of the supplier. When a simple order-up-to policy is used, retailer s order quantity can be expressed as in (1): [ y i y y ( o o )] 1 o (1) t = t 1 2 t 1 + t 2 y1 y 2 In (1), retailer guesses outputs of two processes based on average yield rates and two previous 8

9 order quantities. Then, retailer subtracts from the order-up-to level the beginning inventory and the guessed outputs to get the initial order quantity. However this quantity cannot be used because the random yields. Instead, retailer has to scale up the order quantity by dividing it by product of average yield rates for both processes to compensate the expected loss during the two periods of production. In ISM model, at any given period, retailer receives information from supplier on how much was produced from process 1 and process 2 in the previous period. Retail can incorporate this additional information into its order quantity calculation. Again, when assuming the same simple order-up-to policy is used, retailer s order quantity for ISM model can be expressed as in (2). In ISM model, there is less number of uncertain components associated with calculating the order quantities. [ y i o y o ] 1 o (2) t = t t 2 2 t 1 y1 y 2 Expressions (1) and (2) are used for deciding order quantities each period in our simulations in the next section. 9

10 The objective of the paper is to compare retailer s total average costs of the two models and observe if retailer gains any cost benefits from sharing upstream information in the given supply chain structure. If so, we observe in what operating characteristics the benefit is the most. It is worth noting that these simple order-up-to policies are not optimal for periodic review problem with random yields. However earlier research has shown that they are effective. Since these order-up-to levels cannot be computed analytically, we resort to simulation to obtain our objectives. Simulation Setup Simulation codes are written in VBA based on the models and the sequence of events described in previous sections. Each simulation run has a length of 10,000 periods. Holding cost is charged per item on ending inventory at the end of a period. Penalty cost is charged per item on amount of demand not met by retailer during each period. Amount of demand that is not met in one period are back-logged. Both costs are summed for each period, and total cost is averaged over the length of the run. For generating random numbers for demand and yields, we make sure the same seed is used in each run. Some of the assumptions used in programming the model into simulations are as below: 10

11 - We consider only inventory holding and penalty costs for retailer. - Process time for each process is the same: each takes a single period. - Transportation time between the supplier and the retailer is negligible. To observe the different benefits of sharing upstream information under various operational characteristics of the model we choose, the following three factors are used for the experimental design: 1. Demand variances (4 levels): Lo, Mid-lo, Mid-hi, and Hi - Uniform [Low, Upper]: [100, 100], [75, 125], [50, 150], and [25, 75] - Erlang [Mean, n]: [100, 1], [50, 2], [25, 4], and [12.5, 8] - Normal [Mean, Stdev]: [100, 5], [100, 15], [100, 25], and [100, 35] 2. Random yield variations (3 levels): [-0.1, +0.1], [-0.2, +0.2], and [-0.3, +0.3] (Uniform distribution is used for random yield model with a mean of 0.7) 3. Penalty to holding cost ratio (3 levels): [5, 1], [10, 1], and [15, 1] For the first factor, demand variances, although we use three types of demand distributions, at this stage of the research we only observe aggregate results of these distributions only to see the effects of demand variances. For the second factor, we use the uniform distribution in modeling 11

12 random yield variances, which is one of the simplest forms of representing random yield. When we use a yield variance of +/- 0.1 around a mean of 0.7, it means that the lower and upper bounds of the uniform distribution for random yield are 0.6 and 0.8 respectively. We consider penalty to holding cost ratio as the third factor. We vary the ratio from $5-to-$1 to $15-to-$1 in increment of $5 for penalty cost while holding cost held constant. For each cell of the factorial design, cost improvements are measured when we move from NIS model to ISM model when a simple order-up-to policy is used with an optimal order-up-to level. An optimal order-up-to level for each cell is searched by an algorithm that we developed. Based on an assumption that the cost function is convex, the algorithm searches through different values of order-up-to levels from a given starting point. It searches either forward (increasing) or backward (decreasing) depending on how cost changes from one level to the next. In first round of search, it uses increment of 25 for values of order-up-to level. Once it finds the minimum cost, it goes back by one increment and searches for the second round with increment of 10. In the same way, it continues round 3 and 4 with increments of 5 and 1 respectively. By end of round 4, the algorithm finds the optimal order-up-to level to be used for the simple orderup-to policy to the given cell of the factorial design. With the optimal order-up-to levels used, we are sure that we are comparing the best cost scenarios for both models for cost improvements 12

13 due to information sharing. Results and discussions As the first performance measure, we use percentage cost saving to see relative cost improvements. In percentages, we have cost savings of a range from 1.56% to 7.03% with an average of 3.81% over all the factors (Table 1) when we move from NIS to ISM. Then, we use absolute dollar saving between NIS and ISM models as the next performance measure. Due to the large absolute differences in average costs of the cells, it is difficult to see how the cost improvements behave against certain operational characteristics. It is a lot clearer to see the change in benefits with absolute amounts of dollar saving. A brief summary of results and corresponding plots are shown in Table 1, Table 2, and Figure 2 to Figure 4 below: Table 1. Summary of results: Average percent cost improvements 13

14 Table 2. Summary of results: Average absolute cost improvements Variations in demand variances Variations in yields $6.00 $7.00 $5.00 $6.00 % improvement $4.00 $3.00 $2.00 % improvement $5.00 $4.00 $3.00 $2.00 $1.00 $1.00 $0.00 Lo Mid-Lo Mid-Hi Hi $0.00 +/-.1 +/-.2 +/-.3 Variances Yields Figure 2. Demand variations Figure 3. Yield variations Variations in penalty costs % improvement $4.50 $4.00 $3.50 $3.00 $2.50 $2.00 $1.50 $1.00 $0.50 $ Penalty costs Figure 4. Penalty variations 14

15 From the results, absolute dollar benefits are decreasing in the range from $5.25 (7.03%) to $2.83 (1.56%) as the demand variance increases. This matches with our intuition that information sharing can improve the overall costs only so much as demand variance gets larger. As the yield variance increases from +/- 0.1 to +/- 0.3, the benefits increase from $1.75 (3.06%) to $6.01 (4.31%) with the largest increase being $2.22 (1.25%) from +/- 0.1 to +/ Again, this result matches our intuition: benefits of information sharing get greater as the yield variance gets larger. When penalty to holding costs ratio increases, the benefit of upstream information becomes slightly larger from $3.49 (3.85%) to $4.26 (3.79%) with similar increments between levels: here looking at the percentage values could been misleading because relative percentage savings seem to be decreased although the absolute saving is greater. It seems that benefit of sharing upstream information is not as sensitive to penalty to holding costs ratio as much as to other factors under our experimentation settings. In summary, from our overall observations, upstream information sharing in a two stage supply chain with random yields seems to give a retailer significant cost improvements (1.56% %). Particularly, it is more beneficial to the retailer as demand variation increases, yield variation increases, and penalty to holding cost ratio increases. 15

16 Future Research Is a simple order-up-to policy for random yield problems optimal? Not sure yet. It would not be much worth talking about cost improvements if the selected policy does not result minimal costs of the supply chain. Although, in general, simple order-up-to policy does a good job, we need to verify the optimality of simple order-up-to policy for random yield problems. Two-stage problem will be extended to multiple-stage problem. Two-stage supply chain with longer lead times can also be viewed the same as multiple-stage supply chain. Study on benefits of using different demand distribution types can be done in the future. 16

17 References Chen, F Information Sharing and Supply Chain Coordination in Handbooks in Operations Research and Management Science, 11: Supply Chain Management: Design, Coordination and Operation (Kok and Graves, eds.) North-Holland Gavirneni, S Supply Chain Management at a Chip Test Manufacturer in The Practice of Supply Chain Management (Harrison, Lee, and Neale, eds.), Kluer Academic Publishing (KAP), Yano, C. A., and H. L. Lee Lot Sizing with Random Yields: A Review Opns. Res. 43(2), Nahmias, S Production and Operations Analysis 4 th ed. McGraw-Hill/Irwin 17