We consider a cooperative game defined by an economic lot sizing problem with concave ordering costs over a finite time horizon, in which each player faces demand for a single product in each period and coalitions can pool orders. We show how to compute a dynamic cost allocation in the strong sequential core of this game, i.e. an allocation over time that exactly distributes costs and is stable...

The economic lot scheduling problem (ELSP) addresses the problem of scheduling several items each with its own static, deterministic demand at a single facility, where only one item can be produced at any time. This classical production planning problem has been studied extensively over the last three decades and various heuristic solution methods have been proposed, most of them based on the c...

We study simulation optimization methods for the stochastic economic lot scheduling problem. In contrast to prior research, we focus on methods that treat this problem as a black box. Based on a large-scale numerical study, we compare approximate dynamic programming with a global search for parameters of simple control policies. We propose two value function approximation schemes based on linea...

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A linear description for the economic lot-sizing problem consisting of exponentially many linear inequalities was given by Barany, Van Roy and Wolsey in 1984. Using this formulation we present a dual algorithm for the economic lot-sizing problem, which is of the same complexity as the Wagner and Whitin dynamic programming algorithm. Besides its use in sensitivity analysis the dual algorithm als...

With the growing focus on supply chain management, firms realize that inventories across the entire supply chain can be more efficiently managed through greater cooperation and better coordination. This paper presents a comprehensive and up-to-date review of the joint economic lot sizing problem (JELP) and also provides some extensions of this important problem. In particular, a detailed mathem...

We formulate the well-known economic lot scheduling problem (ELSP) with sequence dependent setup times and costs as a semi-Markov decision process. Using an affine approximation of the bias function, we obtain a semi-infinite linear program determining a lower bound for the minimum average total cost rate. The solution of this problem is directly used in a price-directed dynamic heuristic to de...

In a typical purchasing situation, the issues of price, lot sizing, etc, usually are settled through negotiations between the purchaser and the vendor. Depending on the existing balance of power, the end result of such a bargaining process may be a near-optimal or optimal ordering policy for one of the parties (placing the other in a position of significant disadvantage) or, sometimes, inoptima...