In this paper we develop an economic order quantity model to investigate the optimal replenishment policies for instantaneous deteriorating items under inflation and trade credit. Demand rate is a linear function of selling price and decreases negative exponentially with time over a finite planning horizon. Shortages are allowed and partially backlogged. Under these conditions, we model the ret...

As a practical inventory and transportation problem, it is important to synthesize several objectives for the joint replenishment and delivery (JRD) decision. In this paper, a new multiobjective stochastic JRD (MSJRD) of the one-warehouse and n-retailer systems considering the balance of service level and total cost simultaneously is proposed. The goal of this problem is to decide the reasonabl...

We consider a problem of optimal grouping and provide conditions under which an optimal partition of an ordered set S = {r1, -*t , r,) consists of subsets of consecutive elements. We transform the problem into the problem of finding a shortest path on a directed acyclic graph with n + 1 vertices (for which efficient algorithms exist). These results may be used to solve the problem of grouping n...

We consider several subclasses of the problem of grouping n items (indexed 1, 2, .., n) into m subsets so as to minimize the function g(S 1 , .. , S,). In general, these problems are very difficult to solve to optimality, even for the case m = 2. We provide several sufficient conditions on g(') that guarantee that there is an optimum partition in which each subset consists of consecutive intege...

A novel clustering algorithm is proposed and applied to the multi-item replenishment processing. This new algorithm has two distinguished features: non-binary hierarchical tree and the feature of overlapping clustering. A non-binary hierarchical tree is much smaller than the binary-trees constructed by most traditional algorithms and, therefore, it clearly highlights meaningful clusters which s...

We consider jointly replenishing multiple firms that operate under an EOQ like environment in a decentralized, non-cooperative setting. Each firm’s demand rate and inventory holding cost rate are private information. We are interested in finding a mechanism that would determine the joint replenishment frequency and allocate the joint ordering costs to these firms based on their reported stand-a...

In this paper we present new bounds on the basic cycle time for optimal methods to solve the JRP. They are tighter than the ones reported in Viswanathan [7]. We carry out extensive numerical experiments to compare them and to investigate the computational complexity.

We consider an infinite-horizon deterministic joint replenishment problem with first order interaction. Under this model, the setup transportation/reorder cost associated with a group of retailers placing an order at the same time equals some group-independent major setup cost plus retailer-dependent minor setup costs. In addition, each retailer is associated with a retailer-dependent holding-c...

We introduce an algorithm design technique for a class of combinatorial optimization problems with concave costs. This technique yields a strongly polynomial primal-dual algorithm for a concave cost problem whenever such an algorithm exists for the fixedcharge counterpart of the problem. For many practical concave cost problems, the fixed-charge counterpart is a well-studied combinatorial optim...