# Modeling pooling and perishable items in inventory systems

Abstract: This thesis is built on three papers considering different problems in inventory control. The first paper considers a two-location newsboy model with the possibility of making lateral transshipments when needed. Usually, when considering newsboy models it is assumed that all demand in a period occurs at once. In our model we divide the period into a number of sub-periods, and we assume that there can be demand and transshipments in every sub-period. Furthermore, units can be discarded in each sub-period. This means that the optimal transshipment policy, for instance, varies over time. It means also, that units can be discarded before the end of the period. We provide both an exact solution and an approximate solution to the problem. The exact solution can be implemented if the state space is not too large, while the approximation is preferable when the problem becomes more complex. Our second paper considers a perishable items model with a single product and a single stock location with Poisson demand. The replenishment lead-time from the external supplier is constant. The lifetime is also constant, and aging is assumed to begin when the order is placed. When the age of a unit has reached the end of its lifetime, the unit is useless and thus discarded from the system. The replenishment policy is assumed to be an order-up-to S policy. Demand that cannot be met immediately is backordered. We consider three different models where the service requirements are represented by: 1) a backorder cost per unit, 2) a service level constraint, 3) a backorder cost per unit and time unit. Model 1 and 2 are solved exactly, while an approximation is developed for model 3. We show the results from a paper by Schmidt and Nahmias (1985) can be used to solve the considered problems. Their model differs from ours in that they assume lost sales instead of backordering. The lost sales assumption implies that there will always be exactly S units in the system. Our results are compared to the results in a related paper by Chiu (1995). The third and last paper considers a two-echelon distribution inventory system with a central warehouse and a number of retailers. There is direct customer demand at the warehouse. If this upstream demand requires a high service, it may be advantageous to give higher priority to costumer orders compared to retailer replenishments. We suggest and evaluate techniques for handling this situation. One technique means that we have an extra separate stock for the direct costumer demand at the warehouse. Another technique means that we apply a so-called critical level policy at the warehouse, i.e., if the stock on hand at the warehouse is less than or equal to the critical level, retailer replenishments are backordered.

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