Vendor-managed inventory (VMI) is a supply-chain initiative where the supplier is authorized to manage inventories of agreed-upon stock-keeping units at retail locations. The benefits of VMI are well recognized by successful retail businesses such as Wal-Mart. In VMI, distortion of demand information (known as bullwhip effect) transferred from the downstream supply-chain member (e.g., retailer) to the upstream member (e.g., supplier) is minimized, stockout situations are less frequent, and inventory-carrying costs are reduced. Furthermore, a VMI supplier has the liberty of controlling the downstream resupply decisions rather than filling orders as they are placed. Thus, the approach offers a framework for synchronizing inventory and transportation decisions. In this paper, we present an analytical model for coordinating inventory and transportation decisions in VMI systems. Although the coordination of inventory and transportation has been addressed in the literature, our particular problem has not been explored previously. Specifically, we consider a vendor realizing a sequence of random demands from a group of retailers located in a given geographical region. Ideally, these demands should be shipped immediately. However, the vendor has the autonomy of holding small orders until an agreeable dispatch time with the expectation that an economical consolidated dispatch quantity accumulates. As a result, the actual inventory requirements at the vendor are partly dictated by the parameters of the shipment-release policy in use. We compute the optimum replenishment quantity and dispatch frequency simultaneously. We develop a renewaltheoretic model for the case of Poisson demands, and present analytical results.vendor-managed inventory, freight consolidation, renewal theory

Abstract:In this article, we consider a multi-product closed-loop supply chain network design problem where we locate collection centers and remanufacturing facilities while coordinating the forward and reverse flows in the network so as to minimize the processing, transportation, and fixed location costs. The problem of interest is motivated by the practice of an original equipment manufacturer in the automotive industry that provides service parts for vehicle maintenance and repair. We provide an effective problem formulation that is amenable to efficient Benders reformulation and an exact solution approach. More specifically, we develop an efficient dual solution approach to generate strong Benders cuts, and, in addition to the classical single Benders cut approach, we propose three different approaches for adding multiple Benders cuts. These cuts are obtained via dual problem disaggregation based either on the forward and reverse flows, or the products, or both. We present computational results which illustrate the superior performance of the proposed solution methodology with multiple Benders cuts in comparison to the branch-and-cut approach as well as the traditional Benders decomposition approach with a single cut. In particular, we observe that the use of multiple Benders cuts generates stronger lower bounds and promotes faster convergence to optimality. We also observe that if the model parameters are such that the different costs are not balanced, but, rather, are biased towards one of the major cost categories (processing, transportation or fixed location costs), the time required to obtain the optimal solution decreases considerably when using the proposed solution methodology as well as the branch-and-cut approach.

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Abstract:One of the basic assumptions of the classical dynamic lot-sizing model is that the aggregate demand of a given period must be satisfied in that period. Under this assumption, if backlogging is not allowed then the demand of a given period cannot be delivered earlier or later than the period. If backlogging is allowed, the demand of a given period cannot be delivered earlier than the period, but can be delivered later at the expense of a backordering cost. Like most mathematical models, the classical dynamic lot-sizing model is a simplified paraphrase of what might actually happen in real life. In most real life applications, the customer offers a grace period -we call it a demand time window -during which a particular demand can be satisfied with no penalty. That is, in association with each demand, the customer specifies an earliest and a latest delivery time. The time interval characterized by the earliest and latest delivery dates of a demand represents the corresponding time window. This paper studies the dynamic lot-sizing problem with demand time windows and provides polynomial time algorithms for computing its solution. If shortages are not allowed, the complexity of the proposed algorithm is O(T 2 ). When backlogging is allowed, the complexity of the proposed algorithm is O(T 3 ).2