On the complexity of the economic lot-sizing problem with remanufacturing options

In this paper we investigate the complexity of the economiclot-sizing problem with remanufacturing (ELSR) options. Whereas inthe classical economic lot-sizing problem demand can only besatisfied by production, in the ELSR problem demand can also besatisfied by remanufacturing returned items. Although the ELSRproblem can be solved efficiently for some special cases, we showthat the problem is NP-hard in general, even under stationary costparameters.remanufacturing;complexity;lot-sizing

Four equivalent lot-sizing models

We study the following lot-sizing models that recently appeared in the literature: a lot-sizing model with aremanufacturing option, a lot-sizing model with production time windows, and a lot-sizing model with cumulativecapacities. We show the equivalence of these models with a classical model: the lot-sizing model with inventory bounds.lot-sizing;equivalent models

A note on a multi-period profit maximizing model for retail supply chain management

In this note we present an efficient exact algorithm to solve the joint pricing and inventoryproblem for which Bhattacharjee and Ramesh (2000) proposed two heuristics. Our algorithmappears to be superior also in terms of computation time. Furthermore, we point out several mistakes in the paper by Bhattacharjee and Ramesh.pricing;inventory;dynamic programming

A Polynomial Time Algorithm for a Deterministic Joint Pricing and Inventory Model

In this paper we consider the uncapacitated economic lot-size model, where demand is adeterministic function of price. In the model a single price need to be set for all periods. Theobjective is to find an optimal price and ordering decisions simultaneously. In 1973 Kunreuther and Schrage proposed an heuristic algorithm to solve this problem. The contribution of our paper is twofold. First, we derive an exact algorithm to determine the optimal price and lot-sizing decisions. Moreover, we show that our algorithm boils down to solving a number of lot-sizing problems that is quadratic in the number of periods, i.e., the problem can be solved in polynomial time.pricing;inventory;production;lot-sizing

Worst case analysis for a general class of on-line lot-sizing heuristics.

In this paper we analyze the worst case performance of heuristics for the classical economic lot-sizing problem with time-invariant cost parameters. We consider a general class of on-line heuristics that is often applied in a rolling horizon environment. We develop a procedure to systematically construct worst case instances for a fixed time horizon and use it to derive worst case problem instances for an infinite time horizon. Our analysis shows that any on-line heuristic has a worst case ratio of at least 2. Furthermore, we show how the results can be used to construct heuristics with optimal worst case performance for small model horizons.

On the complexity of the economic lot-sizing problem with remanufacturing options

In this paper we investigate the complexity of the economic lot-sizing problem with remanufacturing (ELSR) options. Whereas in the classical economic lot-sizing problem demand can only be satisfied by production, in the ELSR problem demand can also be satisfied by remanufacturing returned items. Although the ELSR problem can be solved efficiently for some special cases, we show that the problem is NP-hard in general, even under stationary cost parameters

Economic lot-sizing games

In this paper we introduce a new class of OR games: economic lot-sizing (ELS) games.There are a number of retailers that have a known demand for a fixed number of periods.To satisfy demand the retailers order products at the same manufacturer. By placing jointorders instead of individual orders, costs can be reduced and a cooperative game arises. In this paper we show that ELS games are balanced. Furthermore, we show that two specialclasses of ELS games are concave.Game Theory;Lot-sizing;Inventory;Production

A Polynomial Time Algorithm for a Deterministic Joint Pricing and Inventory Model

In this paper we consider the uncapacitated economic lot-size model, where demand is a deterministic function of price. In the model a single price need to be set for all periods. The objective is to find an optimal price and ordering decisions simultaneously. In 1973 Kunreuther and Schrage proposed an heuristic algorithm to solve this problem. The contribution of our paper is twofold. First, we derive an exact algorithm to determine the optimal price and lot-sizing decisions. Moreover, we show that our algorithm boils down to solving a number of lot-sizing problems that is quadratic in the number of periods, i.e., the problem can be solved in polynomial time