The theory on multi-echelon production/inventory systems is a core theory within supply chain management. It provides useful insights for design of supply chains and may be used for tactical and operational planning decisions. The multi-echelon theory started with the seminal paper of Clark and Scarf in 1960. In this tutorial, we describe for which systems optimal policies are known, which key ...

This paper studies convergence properties of optimal values and actions for discounted and averagecost Markov Decision Processes (MDPs) with weakly continuous transition probabilities and applies these properties to the stochastic periodic-review inventory control problem with backorders, positive setup costs, and convex holding/backordering costs. The following results are established for MDPs...

From our review on sustainable EOQ inventory models, most researchers did not include carbon emission in the objective function or constraint. In this study, we enrich recent research by incorporating sustainability criteria into model. The study develops an model considering that comes from transportation and warehouse operations. Moreover, also consider imperfect quality items assume complete...

In the classic Economic Order Quantity model the purchasing cost of an order is paid at the time of its receipt. In some cases retailers ask purchasers to pay all or a fraction of the purchasing cost in advance and may allow them to divide the prepayment into several equal-sized parts. In this paper, an economic order quantity model for an evaporating item with partial backordering and partial ...

In this paper, we develop a procedure for selecting a supplier. Suppliers are characterized by their lead time, price and quality (random yield). Each purchased item is acceptable with a given probability and independent of the others. We assume the demands are deterministic with no set-up cost and backordering is allowed. For each supplier, an optimal ordering policy is developed. We prove the...

Rationing is an inventory policy that allows prioritization for different demand classes. This prioritization results in a different service level for each demand class. The mechanism through which the rationing policy is implemented is to stop serving lower priority classes when the inventory on hand drops below a certain critical level. Under this level, only higher priority classes are serve...

This paper examines the cost-reduction effect of “postponed” routing decisions in a two-echelon supply chain. When a delivery vehicle leaves the warehouse with system replenishment quantities, it sequentially makes routing decisions to choose the next retailer to visit. To measure this effect this paper studies combined vehicle routing and inventoryallocation policies designed to minimize total...

In this paper, we consider the pricing and lot-sizing problem for a product subject to general rate of deterioration and partial backordering. We use impatience functions to model backlogging of demand. We show that even when lost sale and backorder costs are present, the problem is well posed in the reduced space. We provide an iterative procedure for solving the overall problem. We describe s...

We study a stationary, single-stage inventory system, under periodic review, with fixed ordering costs and multiple sales levers (such as pricing, advertising, etc.). We show the optimality of (s, S)-type policies in these settings under both the backordering and lost-sales assumptions. Our analysis is constructive, and is based on a condition which we identify as being key to proving the (s, S...