An index policy for a stochastic scheduling model with improving/deteriorating jobs

We consider stochastic scheduling models which have the natural character that jobs improve while being processed, but deteriorate (and may possibly leave the system altogether) while processing is diverted elsewhere. Such restless bandit problems are shown to be indexable in the sense of Whittle. A numerical study which elucidates the strong performance of the resulting index policy is complemented by a theoretical study which demonstrates the optimality of the index policy under given conditions and which develops performance guarantees for the index heuristic more generally. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 706–721, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10036     

Continuous accumulation games on discrete locations

In an accumulation game, a HIDER attempts to accumulate a certain number of objects or a certain quantity of material before a certain time, and a SEEKER attempts to prevent this. In a continuous accumulation game the HIDER can pile material either at locations $1, 2, …, n, or over a region in space. The HIDER will win (payoff 1) it if accumulates N units of material before a given time, and the goal of the SEEKER will win (payoff 0) otherwise. We assume the HIDER can place continuous material such as fuel at discrete locations i = 1, 2, …, n, and the game is played in discrete time. At each time k > 0 the HIDER acquires h units of material and can distribute it among all of the locations. At the same time, k, the SEEKER can search a certain number s < n of the locations, and will confiscate (or destroy) all material found. After explicitly describing what we mean by a continuous accumulation game on discrete locations, we prove a theorem that gives a condition under which the HIDER can always win by using a uniform distribution at each stage of the game. When this condition does not hold, special cases and examples show that the resulting game becomes complicated even when played only for a single stage. We reduce the single stage game to an optimization problem, and also obtain some partial results on its solution. We also consider accumulation games where the locations are arranged in either a circle or in a line segment and the SEEKER must search a series of adjacent locations. © 2002 John Wiley & Sons, Inc. Naval Research Logistics, 49: 60–77, 2002; DOI 10.1002/nav.1048     

Multi‐item capacitated lot‐sizing problems with setup times and pricing decisions

We study a multi‐item capacitated lot‐sizing problem with setup times and pricing (CLSTP) over a finite and discrete planning horizon. In this class of problems, the demand for each independent item in each time period is affected by pricing decisions. The corresponding demands are then satisfied through production in a single capacitated facility or from inventory, and the goal is to set prices and determine a production plan that maximizes total profit. In contrast with many traditional lot‐sizing problems with fixed demands, we cannot, without loss of generality, restrict ourselves to instances without initial inventories, which greatly complicates the analysis of the CLSTP. We develop two alternative Dantzig–Wolfe decomposition formulations of the problem, and propose to solve their relaxations using column generation and the overall problem using branch‐and‐price. The associated pricing problem is studied under both dynamic and static pricing strategies. Through a computational study, we analyze both the efficacy of our algorithms and the benefits of allowing item prices to vary over time. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

Doubly Stochastic Sequential Assignment Problem

This article introduces the Doubly Stochastic Sequential Assignment Problem (DSSAP), an extension of the Sequential Stochastic Assignment Problem (SSAP), where sequentially arriving tasks are assigned to workers with random success rates. A given number of tasks arrive sequentially, each with a random value coming from a known distribution. On a task arrival, it must be assigned to one of the available workers, each with a random success rate coming from a known distribution. Optimal assignment policies are proposed for DSSAP under various assumptions on the random success rates. The optimal assignment algorithm for the general case of DSSAP, where workers have distinct success rate distribution, has an exponential running time. An approximation algorithm that achieves a fraction of the maximum total expected reward in a polynomial time is proposed. The results are illustrated by several numerical experiments. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 124–137, 2016     

Capacity expansion and cost efficiency improvement in the warehouse problem

The warehouse problem with deterministic production cost, selling prices, and demand was introduced in the 1950s and there is a renewed interest recently due to its applications in energy storage and arbitrage. In this paper, we consider two extensions of the warehouse problem and develop efficient computational algorithms for finding their optimal solutions. First, we consider a model where the firm can invest in capacity expansion projects for the warehouse while simultaneously making production and sales decisions in each period. We show that this problem can be solved with a computational complexity that is linear in the product of the length of the planning horizon and the number of capacity expansion projects. We then consider a problem in which the firm can invest to improve production cost efficiency while simultaneously making production and sales decisions in each period. The resulting optimization problem is non‐convex with integer decision variables. We show that, under some mild conditions on the cost data, the problem can be solved in linear computational time. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 367–373, 2016     

Economic ordering quantities for recoverable item inventory systems

We study a deterministic EOQ model of an inventory system with items that can be recovered (repaired/refurbished/remanufactured). We use different holding cost rates for manufactured and recovered items, and include disposal. We derive simple square root EOQ formulas for both the manufacturing batch quantity and the recovery batch quantity.     

Open shop scheduling to minimize the number of late jobs

We develop polynomial algorithms for several cases of the NP-hard open shop scheduling problem of minimizing the number of late jobs by utilizing some recent results for the open shop makespan problem. For the two machine common due date problem, we assume that either the machines or the jobs are ordered. For the m machine common due date problem, we assume that one machine is maximal and impose a restriction on its load. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 525–532, 1998     

On the use of lexicographic min cost flows in evacuation modeling

Building evacuation problems can be represented as dynamic network-flow problems [3]. The underlying network structure of a building evolves through time yielding a time-expanded network (a dynamic network). Usually in such evacuation problems involving time, more than one objective function is appropriate. For example, minimizing the total evacuation time and evacuating a portion of the building as early as possible are two such objectives. In this article we show that lexicographical optimization is applicable in handling such multiple objectives. Minimizing the total evacuation time while avoiding cyclic movements in a building and “priority evacuation” are treated as lexicographical min cost flow problems.     

Diffusion approximation to the G/G/R machine repair problem with warm standby spares

The G/G/R machine repair problem with M operating machines, S warm standby spares, and R repairmen is studied as a diffusion process. The steady-state equations are formulated as diffusion equations subject to two reflecting barriers. The approximate diffusion parameters of the diffusion equations are obtained (1) under the assumption that the input characteristics of the problem are defined only by their first two moments rather than their probability distribution function, (2) under the assumption of heavy traffic approximation, that is, when queues of failed machines in the repair stage are almost always nonempty, and (3) using well-known asymptotic results from renewal theory. Expressions for the probability density functions of the number of failed machines in the system are obtained. A study of the derived approximate results, compared to some of the exact results, suggests that the diffusion approach provides a useful method for solving complex machine-repair problems.