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The impact of information sharing in two-echelon supply chains R. Nachmias and M. Kaspi Department of Industrial Engineering and Management, Ben-Gurion University, Beer-Sheva, Israel Information sharing in supply chains is important in order to minimize the bullwhip effect, minimize individual organization or global supply chain costs, and improve supply chain efficiency and consumer service levels. In order to measure the impact of information sharing, a simple two-echelon supply chain consisting of a single retailer and a single supplier is considered. The retailer is selling product having Poisson distributed customer demand. The supplier decides when to start manufacturing to meet the retailer's order, in order to minimize inventory holding costs and shortage penalty costs. Two information sharing scenarios were considered: the retailer is not sharing any information with the supplier, and the retailer informs the supplier about its inventory level at each time period. A numerical comparison established indicated a mean supplier cost saving of 22% when information was shared. infinite capacity supplier can benefit by 1. Introduction Supply chains are an inseparable factor sharing information of retailer inventory in everything related to consumerism. The levels while using a batch ordering policy, members of the supply chain incur costs by mean cost savings of 2.2%, with a resulting from strong interactions with maximum of 12.1%. Gavirneni (2006) other chain members, and have an interest, found that the total supply chain costs can individually or in common with other be reduced on average 5% and up to members, in making as many procedures 16.3%, when information on retailer as they are able in order to maximizing inventory levels is shared with the supplier. their revenues. Information sharing is one This work considered a simple two- way. echelon supply chain consisting of a single shared retailer and single supplier. Any order from information to improve the supplier’s order the supplier contains a constant quantity of quantity decisions in a serial system with a product, and the production process time known autoregressive demand process and length of the retailer's order is a single time lowered supply chain costs by about 23%. period. The distribution time is negligible Cachon and Fisher (2000) found that the and there are no capacity constraints. Lee et al. (2000) used Nachmias and Kaspi When a shortage appears at the retailer's p Shortage penalty (per single time period and for single product). organization, the retailer is not obligated to supply the product later. The inventory holding costs are paid when production is 2. Non-Information Model Sharing finished before receiving an order from the Process sequence: The retailer sells the retailer; the shortage penalty costs are paid product to customers. Every time period when production is finished after receiving (in a discrete time) the retailer surveys its an the inventory. As the retailer's inventory is production process is started immediately. depleted, an order, having a fixed quantity Therefore, the shortage penalty costs are of product, is sent to the supplier. At time paid for a single time period only. The period product is delivered when the order is scheduling decision, the supplier starts placed by the retailer and the production manufacturing the products. order. process is As shortage completed. occurs, A numerical comparison for measuring the impact of the full information-sharing model compared to the non-information-sharing model is established. Notations Q Fixed quantity of product ordered by the retailer. Average consumer's demand per single time period. Tp Rc Tc Production process starting time period (supplier decision variable on the noninformation sharing model). The critical retailer's inventory level triggering the start of the production process (supplier's decision variable on the full information sharing model). The first time period when retailer's inventory level equals Rc or less (on the full information sharing model). To The time period when the retailer established an order. h Inventory holding cost (per single time period and for single product). Tp , according Retailer Order Function to Request supplier Probability Defined as PNon To . The probability of having demand for at least Q number of products at time period To , but not before. Expected Time Sequential Orders Length between Defined as ETBSONon Tp . In the case when the retailer's order time period follows the production process starting time period, the cycle ends as the order is requested by the retailer. In the case that the retailer’s order request time period precedes the production process completion time, the cycle ends as the production process is completed. In the latter case, the production process is started immediately when the order is requested. Nachmias and Kaspi Inventory Holding Cost Function process after the order is requested. IHC Non Tp probability of finishing the production P To To Tp 1 h Q To Tp 2 Non Non-Information Sharing Model Total Cost Function Analysis ETBSO Non Tp time periods elapsed from production Costs where To Tp 1 indicates the number of process completion until the order is requested by the retailer. The average Production Process Starting Time Period (Tp) inventory holding cost per single time period is generated with cost function is a Quasi-Convex function. Shortage Penalty Cost Function Tp SPC Non Tp Shortage Penalty Costs Total Costs deviation ETBSO Non Tp . The inventory holding P To p Q To 1 Inventory Holding Costs Non Figure (1) Non-Information Sharing Model, Total Cost Function. 3. Full Information Model Sharing Process sequence: The retailer sells the products to customers. Every time period ETBSO Non Tp (in a discrete time) the retailer surveys its The average shortage penalty cost per inventory and informs the supplier. As the single time period is generated with retailer's inventory is depleted, an order deviation ETBSO Non Tp . The shortage request, having a fixed quantity of product, penalty cost function is a Quasi-Convex function. Total Cost Function The total cost function is a combination of the inventory holding cost and shortage penalty cost functions and is also seen as a Quasi-Convex function. is sent to a supplier. Using the information shared, the supplier decides when to start the production process, according to an initially chosen critical inventory level, Rc . Retailer Order Function Defined as: Request Probability PFull Tc, To . The As the production process starting time probability of having demand for at least period Tp increases, the inventory holding Q Rc number of products at time period costs decrease and the shortage penalty Tc , but not before, along with the costs increase, due to the later production probability of having demand for at least process, and therefore having a greater Q quantity of product at time period To , Nachmias and Kaspi but not before. the critical level Rc , the retailer's inventory Expected Time Sequential Orders Length between level should be equal to 0 (i.e., To Tc ). The average shortage penalty cost per Defined as: ETBSOFull Rc . In the case when the retailer's order request time single time period is generated with the deviation ETBSO Full Rc . The shortage period follows the production process penalty cost function is a Quasi-Convex starting time period, the cycle ends as the function. order is requested by the retailer. In the Total Cost Function case when the retailer’s order request time period precedes the production process completion time period, the cycle ends as the production process is completed. In the latter case, the production process is started immediately when the order is requested. Inventory Holding Cost Function IHC Full ( Rc ) P Tc, To To Tc 1 h Q Tc 1 To Tc 2 Full ETBSO Full Rc The total cost function is a combination of the inventory holding cost and shortage penalty cost functions and seems to be a Quasi-Convex function. As the critical inventory level Rc increases, the inventory holding cost increases and the shortage penalty cost decreases due to the supplier have started the production process earlier and therefore having a greater probability of finishing production before the order is where To Tc 1 indicates the number of issued. time periods passed from starting the Full Information Sharing Model Total Cost Function Analysis production process until receiving an order from the retailer. The average inventory generated with the deviation Costs holding cost per single time period is ETBSO Full Rc . The Inventory holding Critical Inventory Level (Rc) cost function is a Quasi-Convex function. Shortage Penalty Cost Function Inventory Holding Costs Figure (2) SPC Full ( Rc ) P Tc, To Tc p Q Tc 1 Shortage Penalty Costs Total Costs Full Information Sharing Model; Total Cost Function. Full ETBSO Full Rc Remark: In the model environment defined, the first indication about the In order to have shortage, on the first retailer's inventory level is established only detection of retailer's inventory level below at the first time period. The supplier has to Nachmias and Kaspi consider a scheduling policy of starting the 67.91%, while in some cases there were no production (as cost savings at all. Analyzing the cost starting production at time period Tp 0 savings conclusions histogram indicates on the non-information sharing model). 38% of the numerical comparisons resulted During the numerical comparison this case in no impact or a small impact, up to 5%, is considered. by having information sharing. The rest of process immediately the examples resulted in an impact of 5% 4. Numerical Comparison to 70% distributed Normally. In order to measure the impact of information sharing in the supply chain models discussed in this work, a numerical In The Case of Q ~~ The greatest information sharing impact was achieved in the case when comparison has been analyzed. inventory holding cost ( h ) is about the The simulation established is based on shortage penalty ( p ). As the difference random environmental parameter values and not on predetermined values ( is between the inventory holding cost ( h ) between 0 and 10; Q is between and and the shortage penalty ( p ) increases, the 40; h and p are between 0 and 1), and was replicated over 7000 times. Two cases impact of information sharing decreases. Generally the optimal production are distinguished; the first is the case process schedule is at an earlier time where the fixed quantity of product period on the non-information sharing ordered average model or at high critical inventory level on consumer's demand ( ) (Q is less than the full information sharing model. In the 2 ; defined as: Q ~~ ), and the second case when the inventory holding cost ( h ) (Q ) is about the is the case where the fixed quantity of product ordered ( Q ) is significantly greater than the average consumer's is significantly less than the shortage penalty ( p ), the optimal time period for starting production ( Tp * ) converges to 0 demand ( ) ( Q is greater than 2 ; and the optimal critical inventory level defined as: Q ). ( Rc * ) converges to Q or immediately (at time The results of the period 0), generating similar numerical scheduling on both models and therefore, comparison indicate a mean cost savings of the impact of information sharing is very 22.28% in the case of having information small. sharing. The maximum cost savings was Nachmias and Kaspi In The Case of Q cost ( h ) is significant greater than the The largest information sharing impact shortage penalty ( p ), the optimal time is achieved in the case when the inventory period for starting production ( Tp * ) is holding cost ( h ) is less than the shortage much greater then Q and the optimal penalty ( p ). Generally, as the difference critical inventory level ( Rc * ) is less then between the inventory holding cost ( h ) , and the shortage penalty ( p ) increases, the production impact of information sharing decreases. completed with receipt of the retailer's generating policies process will where the probably be order or having a single shortage time In the case when the inventory holding cost ( h ) is significantly less than the period and, therefore, the impact of information sharing is small. shortage penalty ( p ), while the difference between the fixed quantity of product As the fixed quantity of product ordered ( Q ) and the average consumer's ordered ( Q ) converges to the average demand ( ) is small, the optimal time consumer's demand ( ), the information period for starting production ( Tp * ) sharing impact decreases. In the case when converges to 0 and the optimal critical inventory level ( Rc * ) converges to Q or immediately, generating similar scheduling on both models and, therefore, the impact of information sharing is very small. As the relation between the fixed quantity of product ordered ( Q ) and the average the fixed quantity of products ordered ( Q ) is significantly greater than the average consumer's demand ( ), the information sharing impact decreases also. 5. References [1] Cachon Ge´rard, Fisher Marshall. (2000). Supply Chain Inventory Management consumer's demand ( ) increases, the and optimal time period for starting production Management Science, Vol. 46, 8, 1032–1048. ( Tp * ) increases and the optimal critical [2] the value of Gavirneni Shared Information. Srinagesh, Roman inventory level ( Rc * ) decreases; however, Kapuscinski, Sridhar Tayur. (1999). Value of the critical inventory level gives a better information in capacitated supply chains. prediction of the retailer's order request Management Science, Vol. 45, 1, 16–24. time period and, therefore, the impact of information sharing increases. In the case when the inventory holding [3] Lee Hau, So Kut, Tang Christopher. (2000). The Value of Information Sharing in a Two-Level Supply Chain. Science, Vol. 46, 5, 626–643. Management