Chia-Shin Chung

A branch and bound algorithm to minimize the total weighted flowtime for the two-stage assembly scheduling problem

In this paper, a two-stage assembly scheduling problem is considered with the objective of minimizing the total weighted flowtime. A lower bounding procedure and a dominance criterion are developed and incorporated into a branch and bound procedure. A heuristic procedure is also used to derive an initial upper bound. Computational results of the algorithm are presented.

A branch and bound algorithm to minimize the total flow time for m-machine permutation flowshop problems

Abstract The m -machine permutation flowshop problem with the total flow-time objective is a common scheduling problem, which is known to be NP-hard for m ⩾2. In this article, we develop a branch and bound algorithm to solve both the weighted and unweighted version of this problem. Our algorithm incorporates a new machine-based lower bound and a dominance test for pruning nodes. Computational experiments suggest that the algorithm can handle test problems with n ⩽15. It also seems capable of dealing with larger problems for the unweighted objective, especially when the processing times are correlated.

A multi-item newsvendor problem with preseason production and capacitated reactive production

Abstract Given items with short life cycles or seasonal demands, one can potentially improve profits by producing during the selling season, especially when its production capacity is substantial. We develop a two-stage, multi-item model incorporating reactive production that employs a firm’s internal capacity . Production occurs in an uncapacitated preseason stage and a capacitated reactive stage . Demands occur in the reactive stage. Reactive capacities are pre-allocated to each item in the preseason stage and cannot be changed during the reactive stage. Reactive production occurs during the selling season with full knowledge of demands. The objective is expected profit maximization. Unsatisfied demand is lost. The revenue, salvage value, and production and lost sales costs are proportional. Assuming no fixed costs, we present a simple algorithm for computing optimal policies. For a model with fixed costs for allocating preseason stage production and reactive stage capacity to product families, we characterize optimal policies and develop optimal and heuristic algorithms.

The coordinated replenishment dynamic lot-sizing problem with quantity discounts

Abstract In the classical coordinated replenishment dynamic lot-sizing problem, the primary motivation for coordination is in the presence of the major and minor setup costs. In this paper, a separate element of coordination made possible by the offer of quantity discounts is considered. A mathematical programming formulation for the extended problem under the all-units discount price structure and the incremental discount price structure is provided. Then, using variable redefinitions, tighter formulations are presented in order to obtain tight lower bounds for reasonable size problems. More significantly, as the problem is NP-hard, we present an effective polynomial time heuristic procedure, for the incremental discount version of the problem, that is capable of solving reasonably large size problems. Computational results for the heuristic procedure are reported in the paper.

A heuristic algorithm for determining replacement policies in consecutive k -out-of- n systems

This article presents a heuristic algorithm for determining replacement policies in a discrete-time, infinite-horizon, dynamic programming model of a binary coherent system with n statistically independent components, and then specializes the algorithm to consecutive k-out-of-n systems. Costs arise when the system fails and when failed components are replaced. The objective is to minimize the long run expected average undiscounted cost per period. A companion article (Naval Res. Logistics 49 (2002) 288) develops a branch and bound algorithm for computing optimal policies. Extensive computational experiments on consecutive k-out-of-n systems find it effective when n≤ 40 or k is near n; however, the computations can be intractable when n > 40 and 2≤k < n-15, suggesting the need for a good heuristic. Computational experiments on consecutive k-out-of-n systems involving over 300,000 test problems find the heuristic of this article highly effective. For each n and k tested, its percentage error was under 2.53%, and its mean computation time on a 1700 MHz Pentium IV was under 0.24 s (the largest n in our experiments was 200).

A newsboy problem with reactive production

Abstract This paper extends the classic newsboy problem by introducing reactive production . Production occurs in two stages, a anticipatory stage and a reactive stage . In the anticipatory stage, one determines a production level that anticipates the demand, all of which occurs in the reactive stage. There production takes place with full knowledge of the actual demand and, thus, can react to it. The reactive stage contains multiple sources of capacitated production. Demand is continuous and stochastic, and production, holding, and shortage costs are proportional. There are no fixed costs. Shortages are lost. Our model reduces to a single-period model with piecewise-linear convex costs. We obtain an analogue of the well-known critical fractile formula of the classic newsboy model. We also undertake a numerical study that compares our model with (i) the classic newsboy model, and (ii) a model which employs reactive production but uses classic newsboy formulas. Extensive computational experiments with normal demand problems suggest that the costs under our model can be substantially less than the costs under (i) and (ii). Scope and purpose Consider a seasonal product with a long-selling season and a highly volatile stochastic demand. The classic newsboy formulation of this problem assumes that all unsold goods be salvaged at a price that is often far below the production cost. This could lead to unacceptably low service levels since it tends to discourage high stock levels. On the other hand, were management to raise the service level to an acceptable level, the cost of the safety stock might be too great because of the highly volatile demand. To address this difficulty, we modify the classic newsboy problem by allowing management to schedule production in reaction to the demand during the selling period. Such production is possible when the selling period encompasses a long time interval. Our results indicate that this modification can significantly improve both costs and service levels.

The newsvendor problem with an in-season price adjustment

Consider a retailer stocking a seasonal item facing a stochastic demand where information about the demand becomes more accurate as the selling season progresses. The retailer places orders before the start of the season and in-season reorders are not possible. This article extends the classical newsvendor model by allowing the retailer to make an in-season price adjustment after conducting a review and using the realized demand to obtain an accurate estimate of the remaining demand. Our results include answers to the following questions. What price should the retailer choose? How much should the retailer have ordered at the start of the season given the option of adjusting prices in-season? This model was motivated by a problem in car rental revenue management and has applications in perishable assets revenue management (PARM), where price adjustments are needed towards the end of the selling season.

A hard knapsack problem

In this article we develop a class of general knapsack problems which are hard for branch and bound algorithms. The number of alternate optimal solutions for these problems grows exponentially with problem parameters. In addition the LP bound is shown to be ineffective. Computational tests indicate that these problems are truly difficult for even very small problems. Implications for the testing of algorithms using randomly generated problems is discussed.

A single-period inventory placement problem for a supply system with the satisficing objective

Consider the inventory placement problem in an N-stage supply system facing a stochastic demand for a single planning period. Each stage is a stocking point holding some form of inventory (e.g., raw materials, subassemblies, product returns or finished products) that after a suitable transformation can satisfy demand. Stocking decisions are made before demand occurs. Unsatisfied demands are lost. The revenue, salvage value, ordering, transformation, and lost sales costs are proportional. There are fixed costs for utilizing stages for stock storage. The objective is to maximize the probability of achieving a given target profit level.

Optimal replacement policies for a multicomponent reliability system

This paper studies a discrete time, infinite horizon, dynamic programming model for the replacement of components in a binary coherent system. Under quite general conditions, we show that it is optimal to follow a critical component policy (CCP), i.e., a policy specified by a critical component set and the rule: Replace a component if and only if it is failed and in the critical component set. We also discuss the problem of computing such policies.