André Gascon

A dynamic programming solution to the dynamic, multi-item, single-machine scheduling

This article presents a dynamic programming algorithm for scheduling, on a single machine, production of multiple items with time-varying deterministic demands. We formulate the scheduling problem with the objective of minimizing the sum of changeover and inventory holding costs. The formulation is appealing in that it represents changeover costs directly instead of by the familiar approximate technique of including setup costs in the objective. Our algorithm, which we developed using an approach similar to C. R. Glasseys that minimizes the total number of changeovers, casts the optimal schedule as a shortest path through a network embedded in a state space. It generates optimal schedules under two assumptions. First, we assume that in each time period within the planning horizon, the machine must either be shut down or be producing some one item for the entire time period. Second, we assume that inventory holding costs are representable as a nondecreasing function of aggregate inventory. We provide a number of numerical examples that we solved using the algorithm.

On the finite horizon EOQ model with cost changes

In this note, an algorithm previously introduced by B. Lev and H. Weiss to optimally solve the finite horizon EOQ model with price changes is modified to avoid infeasible solutions. An example is provided.

Dynamic lot-sizing with price changes and price-dependent holding costs

Abstract This paper proposes a new formulation of the dynamic lot-sizing problem with price changes which considers the unit inventory holding costs in a period as a function of the procurement decisions made in previous periods. In Section 1, the problem is defined and some of its fundamental properties are identified. A dynamic programming approach is developed to solve it when solutions are restricted to sequential extreme flows, and results from location theory are used to derive an O( T 2 ) algorithm which provides a provably optimal solution of an integer linear programming formulation of the general problem. In Section 2, a heuristic is developed for the case where the inventory carrying rates and the order costs are constant, and where the item price can change once during the planning horizon. Permanent price increases, permanent price decreases and temporary price reductions are considered. In Section 3, extensive testing of the various optimal and heuristic algorithms is reported. Our results show that, in this context, the two following intuitive actions usually lead to near optimal solutions: accumulate stock at the lower price just prior to price increase and cut short on orders when a price decrease is imminent.

Solving a one-dimensional cutting-stock problem in a small manufacturing firm: a case study

This paper presents an evaluation of four different sequential approaches to solving the one-dimensional cutting-stock problem in an industrial setting where trim loss and pattern changes costs are of importance. The evaluation is made with sample problems generated from data of a manufacturing company as well as with real problems. Triangular distributions, which are representative of many practical environments, are introduced as proxies to the distribution of the lengths required. Conclusions are drawn based on the various problem sizes and distributions tested.

The Lookahead Heuristic For Multi-Item Single Machine Production Scheduling With Dynamic, Stochastic Demands

AbstractThis paper presents a simple heuristic for scheduling the production of many items on a single machine when demands are both dynamic and stochastic. The heuristic is based on {s, S) type policies and relies principally on simulations of the upcoming production days (the Lookahead function) to decide if the production facility should be shut down or not on a given working shift. Comparative simulation test results show that, under varying production conditions, the Lookahead heuristic provides low total inventory and changeover costs while maintaining high service level.

Computer-assisted multi-item, muti-machine and multi-site scheduling in a hardwood flooring factory

Within this paper, we consider the problem of supporting the scheduling of a set of lumber drying kilns as to meet the demand generated by the production plan of a hardwood factory, while avoiding stockouts. The computer-based coordination of the kiln-drying activities within the global hardwood flooring production process is first presented. Then, we focus on the kiln drying activities and develop a heuristic to schedule kilns in a multi-item, multi-machine and multi-site production environment, with the objective of keeping inventories low while meeting demand and avoiding stockouts. An overview of KilnOpt, an object-oriented software environment to implement the scheduling heuristic is presented in the last section of the paper.

A note on improving the performance of the enhanced dynamic cycte lengths heuristic for the multi-item, single machine scheduling problem

A comparison of different heuristics to schedule the multi-item, single-machine problem with stochastic, time-varying demands was previously performed by Gascon, Leachman and Lefran90is. In this note, we show how the performance of one of these heuristics, the Enhanced Dynamic Cycle Lengths heuristic, can be improved and thus dominate all the other heuristics in all the various test cases simulated.