Minimizing flow time on a single machine with job classes and setup times

We examine the static sequencing problem of ordering the processing of jobs on a single machine so as to minimize the average weighted flow time. It is assumed that all jobs have zero ready times, and that the jobs are grouped into classes with the property that setup tasks are only required when processing switches from jobs of one class to jobs of another class. The time required for each setup task is given by the sum of a setdown time from the previous class and a setup time for the new class. We show that an algorithm presented in the literature for solving a special case of this problem gives suboptimal solutions. A number of properties of the optimal solution are derived, and their use in algorithms is evaluated. Computational results are presented for both a branch-and-bound procedure and a simpler depth-first search.     

Optimal inventory policies for substitutable commodities with stochastic demand

In this article we consider a stochastic model for two products which have a single-period inventory structure and which can be used as substitutes for each other should the need arise. Substitution will occur with probability one, but at perhaps a different revenue level. We prove that the expected profit function is concave, allowing us to find optimal stocking levels for the two products. We compare optimum inventory levels for the case of single substitution with that where there is no substitution. It is demonstrated for the case of single substitution that total optimum order quantities can actually increase or decrease with the substitution revenue.     

A branch-and-bound algorithm for flow-path design of automated guided vehicle systems

An algorithm for determining the optimal, unidirectional flow path for an automated guided vehicle system with a given facility layout is presented. The problem is formulated as an integer program. The objective is to minimize the total distance traveled by vehicles subject to the constraint that the resulting network consists of a single strongly connected component. A specialized branch-and-bound solution procedure is discussed in detail.     

The single period procurement problem where dedicated supplier capacity can be reserved

In this article we consider the single period procurement strategy for an item with uncertainty in its demand and uncertainty in the capacity of the supplier. Dedicated capacity can be ensured by paying a premium charge to the supplier. The other decision variable is the replenishment quantity to request. It turns out to be very easy to select the best value of this latter quantity. On the other hand, we are only able to characterize the general behavior of the expected profit as a function of the level of dedicated capacity. In general, there can be multiple local maxima as a function of the dedicated capacity. However, for the special, but important, case of normally distributed demand, normally distributed capacity and a linear cost for reserving capacity, an algorithm is developed for finding the best level of dedicated capacity. Some preliminary insights regarding the extension to multiple periods are presented. © 1995 John Wiley & Sons, Inc.     

A generalized model for the economic design of x̄control charts for production systems with increasing failure rate and early replacement

This article generalizes the model for the economic design of x̄-control charts of Duncan [4], starting from the more recent papers of Lorenzen and Vance [8] and Banerjee and Rahim [3]. The classical model of Duncan [4] and its several extensions including the unified model of Lorenzen and Vance [8] assumed exponentially distributed in-control periods and provided uniform sampling schemes. Banerjee and Rahim [3], however, assumed a Weibull-distributed in-control period having an increasing failure rate and used variable sampling intervals. The present article is an extension of the work of Banerjee and Rahim [3], where a general distribution of in-control periods having an increasing failure rate is assumed and the possibility of age-dependent repair before failure is considered. Several different truncated and nontruncated probability models are chosen. It is proposed that economic benefits can be achieved by adopting a nonuniform inspection scheme and by truncating a production cycle when it attains a certain age. Numerical examples are presented to support this proposition. Finally, the effect of model specification in the choice of failure mechanism is investigated. © 1993 John Wiley & Sons, Inc.     

A linear relaxation heuristic for the generalized assignment problem

We examine the basis structure of the linear relaxation of the generalized assignment problem. The basis gives a surprising amount of information. This leads to a very simple heuristic that uses only generalized network optimization codes. Lower bounds can be generated by cut generation, where the violated inequalities are found directly from the relaxation basis. An improvement heuristic with the same flavor is also presented.     

Optimal shift scheduling: A branch‐and‐price approach

We present a branch‐and‐price technique for optimal staff scheduling with multiple rest breaks, meal break, and break windows. We devise and implement specialized branching rules suitable for solving the set covering type formulation implicitly, using column generation. Our methodology is more widely applicable and computationally superior to the alternative methods in the literature. We tested our methodology on 365 test problems involving between 1728 and 86400 shift variations, and 20 demand patterns. In a direct comparison with an alternative method, our approach yields significant improvements both in cpu time and in the number of problem instances solved to optimality. The improvements were particularly marked for problems involving larger numbers of feasible shifts. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47: 185–200, 2000     

A nonlinear approach to the multiorigin,multidestination fleet deployment problem

The problem of minimal-cost operation of a fleet of ships carrying a specific amount of bulk cargo from several origin ports to several destination ports during a specified time interval is examined. The fuel oil cost, a major component of the total operating cost, is realistically modeled as a nonlinear function of the vessels' operating speeds. Introduction of both full load and ballast speeds as independent variables results in a nonlinear optimization problem in which the vessels' allocation to the available routes and the optimal speed selection problem are coupled. Within the framework of our model, each vessel of the fleet may load at any origin, unload at a destination and return to the same origin. The solution method developed utilizes specific features of the above fleet deployment model, and may reduce substantially the dimensionality of the problem. Under certain conditions, decoupling of the speed selection from the vessel allocation problem can be achieved, and linear programming can be used to obtain an optimal solution. In the general case, a projected Lagrangian method appears to be more appropriate for the problem under consideration.     

Principal-agent maintenance problem

This article studies a maintenance problem that is applicable for multidivision organizations on lessee-lessor relationships. It is assumed that the parties sign a contract for a fixed time period. Within the period, the lessor is allowed to use the equipment supplied by the lessee. The availability of the equipment that may suffer from breakdown depends on the preventive maintenance policy adopted by the lessor. The properties of this policy as well as other features of the problem are analyzed using a one-period model that takes into account the economic value of the contract as perceived by the lessor and the lessee. The optimal contracting arrangements are analyzed from the perspective of efficient risk sharing and incentive provisions.