We present a two‐period model of remanufacturing in the face of competition. In our model, an original equipment manufacturer (OEM) competes with a local remanufacturer (L) under many reverse logistics configurations for the returned items. After establishing the Nash Equilibrium in the second period sub‐game, we use numerical experiments for comparative statics. OEM wants to increase L'S remanufacturing cost. Surprisingly, while L competes in the sales market, she has incentives to reduce oem's remanufacturing cost. A social planner who wants to increase remanufacturing can give incentives to the OEM to increase the fraction available for remanufacturing, or reduce his remanufacturing costs.
In many practical applications or multi-item inventory systems significant economies of scale can be exploited when coordinating replenishment orders for groups of items. This paper considers a continuous review multi-item inventory system with compound Poisson demand processes; excess demands are backlogged and each replenishment requires a lead time. There is a major setup cost associated with any replenishment of the family of items, and a minor (item dependent) setup cost when including a particular item in this replenishment. Moreover there are holding and penalty costs. We present an algorithm which searches for a simple coordinated control rule minimizing the long-run average cost per unit time subject to a service level constraint per item on the fraction of demand satisfied directly from on-hand inventory. This algorithm is based on a heuristic decomposition procedure and a specialized policy-iteration method to solve the single-item subproblems generated by the decomposition procedure. The model applies to multi-location inventory systems with similar cost structures for coordinated deliveries.multi-item inventory systems, coordinated replenishments, compound Poisson demand processes, service level constraint, policy-iteration algorithm
In many resource allocation problems, the objective is to allocate discrete resource units to a set of activities so as to maximize a concave objective function subject to upper bounds on the total amounts allotted to certain groups of activities. If the constraints determine a polymatroid and the objective is linear, it is well known that the greedy procedure results in an optimal solution. In this paper we extend this result to objectives that are "weakly concave," a property generalizing separable concavity. We exhibit large classes of models for which the set of feasible solutions is a polymatroid and for which efficient implementations of the greedy procedure can be given.
This paper considers an MIG/c queueing system serving a finite number (J) of distinct customer classes. Performance of the system, as measured by the vector of steady-state expected waiting times of the customer classes (the performance vector), may be controlled by adopting an appropriate priority discipline. We show that the performance space, the set of performance vectors which are achievable under some nonpreemptive work conserving priority rule, is a polyhedron described by 2J-1 inequalities. The special (polymatroidal) structure of this polyhedron, nevertheless, allows for efficient (O(J2 log J)) procedures to minimize any convex (separable) function of the performance vector. Linear objectives are shown to be minimized by absolute priority rules, thus generalizing a well-known result for MI G/l systems. We also show that each point in the performance space may be achieved by a unique, generalized dynamic priority rule, specified by J-1 parameters, which may be determined by the recursive solution of J-1 single variable quadratic equations. This class of rules contains the absolute priority rules and the (pure) dynamic rules as special cases. Our results are accurate up to one, extremely accurate, approximation and completely exact for MIGI 1 and MIMIc systems as well as in heavy traffic.
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