Parallel machine scheduling with batch deliveries to minimize total flow time and delivery cost

Motivated by the flow of products in the iron and steel industry, we study an identical and parallel machine scheduling problem with batch deliveries, where jobs finished on the parallel machines are delivered to customers in batches. Each delivery batch has a capacity and incurs a cost. The objective is to find a coordinated production and delivery schedule that minimizes the total flow time of jobs plus the total delivery cost. This problem is an extension of the problem considered by Hall and Potts, Ann Oper Res 135 (2005) 41–64, who studied a two‐machine problem with an unbounded number of transporters and unbounded delivery capacity. We first provide a dynamic programming algorithm to solve a special case with a given job assignment to the machines. A heuristic algorithm is then presented for the general problem, and its worst‐case performance ratio is analyzed. The computational results show that the heuristic algorithm can generate near‐optimal solutions. Finally, we offer a fully polynomial‐time approximation scheme for a fixed number of machines. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 492–502, 2016     

Learning to Fight and Fighting to Learn: Practitioners and the Role of Unit Publications in VIII Fighter Command 1943–1944

A military cannot hope to improve in wartime if it cannot learn. Ideally, in wartime, formal learning ceases and the application of knowledge begins. But this is optimistic. In 1942, USAAF Eighth Air Force assumed it had the means necessary for victory. In reality, its technique and technology were only potentially – rather than actually – effective. What remained was to create the practice of daylight bombing – to learn. This article (1) recovers a wartime learning process that created new knowledge, (2) tests existing tacit hypotheses in military adaptation research, and (3) offers additional theoretical foundation to explain how knowledge is created in wartime     

Interrelationships between performance measures for the machine-repairman problem

The machine-repairman problem with heterogeneous machines and multiple repairmen is considered. It is assumed that machine up times and repair times have general distributions, and a work-conserving service discipline is employed. Under these general assumptions, steady-state relationships between performance measures are examined for the individual machines. Also, various performance measures are defined for the aggregate system and interrelationships between these measures are established.     

Optimal layered search

This article investigates the problem of planning an optimal layered search for a stationary target. A search is layered if it assigns each point in the search space an integer number of glimpses or looks. General necessary and sufficient conditions and an existence theorem are obtained. The special case in which the initial target distribution is bivariate normal is considered in detail.     

Interactive multicriteria linear programming: An extension of the method of Zionts and Wallenius

This article presents an extension of the interactive multicriteria linear-programming method of Zionts and Wallenius [see Management Science, 29 (5) (1983)]. The decision maker's underlying utility function is assumed to be pseudoconcave, and his preference structure is assessed through pairwise comparison questions. In the method of Zionts and Wallenius, the decision maker's preference structure is represented as constraints on the weights on the objectives derived from his responses. This representation is only a linear approximation to the underlying nonlinear utility function. Accordingly, inconsistency among the constraints on the weights arises while solving the problem. Therefore, some of the constraints have to be dropped, resulting in a loss of information on the preference structure, and hence an increase in the total number of questions. In this article we develop a hybrid representation scheme to avoid this problem. The proposed scheme is implemented within the algorithmic framework of the method of Zionts and Wallenius, and its underlying theory is developed. Computational results show that the number of questions required by the Zionts and Wallenius method can be sinificantly reduced using the proposed scheme.     

Facility location on a grid with a diagonal line

This article extends the traditional median problem on a grid to include a diagonal line (e.g., a street). In contrast to the traditional median problem, this generalized problem is nonconvex and nonseparable, invalidating some of the properties on which well-known median-seeking algorithms are based. This work presents an algorithm for finding the median on this generalized grid and discusses the relationship between it and the traditional median.     

Optimal strategies for problems of simultaneous attack against an area defense with impact-point prediction

An area to be defended consists of separated point targets. These targets are subject to an attack in which the offensive weapons are assumed to arrive simultaneously. The defense has area defenders, each of which is capable of intercepting any attacker'. Furthermore, the defense has impact-point prediction, i.e., it has knowledge of each attacker's intended target prior to allocation of the area interceptors. For a given attack, the defense wishes to allocate its interceptors against attackers so as to maximize the expected total survival value of the targets. In its first move, the offense seeks an attack allocation which will minimize expected total surviving value against best defense. We develop an algorithm to determine optimal attack and defense strategies and the optimal value of this sequential min-max problem. Branch-and-bound techniques are used to obtain integer solutions, and illustrative computational results are provided.     

Multi-item service constrained (s,S) policies for spare parts logistics systems

Many organizations providing service support for products or families of products must allocate inventory investment among the parts (or, identically, items) that make up those products or families. The allocation decision is crucial in today's competitive environment in which rapid response and low levels of inventory are both required for providing competitive levels of customer service in marketing a firm's products. This is particularly important in high-tech industries, such as computers, military equipment, and consumer appliances. Such rapid response typically implies regional and local distribution points for final products and for spare parts for repairs. In this article we fix attention on a given product or product family at a single location. This single-location problem is the basic building block of multi-echelon inventory systems based on level-by-level decomposition, and our modeling approach is developed with this application in mind. The product consists of field-replaceable units (i.e., parts), which are to be stocked as spares for field service repair. We assume that each part will be stocked at each location according to an (s, S) stocking policy. Moreover, we distinguish two classes of demand at each location: customer (or emergency) demand and normal replenishment demand from lower levels in the multiechelon system. The basic problem of interest is to determine the appropriate policies (s_i S_i) for each part i in the product under consideration. We formulate an approximate cost function and service level constraint, and we present a greedy heuristic algorithm for solving the resulting approximate constrained optimization problem. We present experimental results showing that the heuristics developed have good cost performance relative to optimal. We also discuss extensions to the multiproduct component commonality problem.     

A periodic maintenance model with used equipment and random minimal repair

The maintenance strategy considered in this article is in the class of block replacement policies. The working unit is replaced by new ones at instants T,2T,3T,… independently of the age and state of the unit. If a failure occurs between these instants, the random repair cost is evaluated. If it is smaller than a predetermined control limit then a minimal repair is carried out. Otherwise the unit is replaced by a used unit. The performance of this maintenance strategy is evaluated in terms of average total cost per time unit over an infinite time span. The mathematical model is defined and several analytical results are obtained. A computer program has been written, which solves the mathematical problem, and some examples are given for the cases where the underlying life distribution is gamma, Weibull or truncated normal.     

The discrete evasion game with three-move lag

The discrete evasion game with three-move lag, formulated over 30 years ago, was one of the earliest games with time-lag complications. This game remains unsolved even though it is well known that the game has a value. In this article we obtain an upper bound for the value by constructing a strategy which consists of 400 conditional probabilities for the minimizing player. This is believed to be the best upper bound known.