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Developing Inventory Control Policies with No Ordering Costs in Two-Echelon Supply Chains

Tayebi, Hamed | 2014

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 45309 (01)
  4. University: Sharif University of Technology
  5. Department: Industrial Engineering
  6. Advisor(s): Haji, Rasoul
  7. Abstract:
  8. This dissertation attempts to develop four inventory control models for two-echelon supply chains. For the all models, the retailers face Poisson demand and lost sales during a stockout. There is also a time-dependent holding cost and a cost per unit of lost sales. However, there is no (or negligible) cost associated with placing an order.
    For the first model, we consider a two-echelon inventory system with one central warehouse and a number of retailers. The central warehouse applies (R, Q) policy and retailers apply base stock policy. In this model, we approximate the arrival process of the central warehouse and obtain the total cost of the system, as well as the optimal solution. Based on this approximation, we present a lower bound function for the total cost of the system and establish its convexity. We use this lower bound to obtain the approximate optimal parameters of the system. Finally, we show the efficiency of our approximation using numerical examples.
    The second model deals with an inventory system with one supplier and two retailers. One retailer can ship items to the other retailer when facing a stock out. Arriving demands to any retailer are lost if he is out-of-stock and it is not possible to initiate an emergency transshipment. Retailers apply one-for-one-period ordering, (1, T), policy. In this new ordering policy which is different from the classical inventory policies, the time interval between any two consecutive orders is fixed and the quantity of each order is one. We derive the long-run average cost and prove its convexity. We present an algorithm to find the optimal solution and minimize the system cost and show that for long lead times, applying (1, T) ordering policy results in a lower cost than (S-1, S) policy, so (1, T) policy is preferred under long lead time condition.
    The next model considers a two-echelon inventory system with one central warehouse and a number of retailers. We assume that each retailer faces an independent Poisson demand with the same rate and applies the common cycle (1, T) ordering policy. In this method, at each cycle, the warehouse orders a batch of size N (number of the retailers) to his own supplier. Upon receipt of each batch he sends 1 unit of the product to each retailer with a fixed transportation cost per cycle (irrespective of the number of retailers). We obtain the optimal time interval between any two consecutive orders.
    For the last model, we relax the assumption of identical customer arrival rate of the previous model, and apply an ordering policy at retailers where a warehouse replenishes one unit item for each retailer in multiples of a base cycle time. Thus, in a given cycle, the warehouse jointly orders to its own supplier the batch in size of the number of the retailers to be served at that given cycle. Immediately upon receipt of each batch, he sends one unit item to these retailers with a fixed transportation cost per cycle. We calculate the total cost of the system, and present a procedure to obtain near optimal values of the base cycle time, and the multiples of the base cycle in which retailers should be served.
  9. Keywords:
  10. Lost Sale ; Two Echelon Inventory Model ; Ordering Policy ; Base Stock Ordering Policy ; Emergency Lateral Transshipment ; Joint Ordering

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