Periodic review inventory management with contingent use of two freight modes with fixed costs

We study a stochastic inventory model of a firm that periodically orders a product from a make‐to‐order manufacturer. Orders can be shipped by a combination of two freight modes that differ in lead‐times and costs, although orders are not allowed to cross. Placing an order as well as each use of each freight mode has a fixed and a quantity proportional cost. The decision of how to allocate units between the two freight modes utilizes information about demand during the completion of manufacturing. We derive the optimal freight mode allocation policy, and show that the optimal policy for placing orders is not an (s,S) policy in general. We provide tight bounds for the optimal policy that can be calculated by solving single period problems. Our analysis enables insights into the structure of the optimal policy specifying the conditions under which it simplifies to an (s,S) policy. We characterize the best (s,S) policy for our model, and through extensive numerical investigation show that its performance is comparable with the optimal policy in most cases. Our numerical study also sheds light on the benefits of the dual freight model over the single freight models. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011     

A note on the single-machine scheduling problem with minimum weighted completion time and maximum allowable tardiness

This paper analyzes the Smith-heuristic for the single-machine scheduling problem where the objective is to minimize the total weighted completion time subject to the constraint that the tradiness for any job does not exceed a prespecified maximum allowable tardiness. We identify several cases of this problem for which the Smith-heuristic is guaranteed to lead to optimal solutions. We also provide a worst-case analysis of the Smith-heuristic; the analysis shows that the fractional increase in the objective function value for the Smith-heuristic from the optimal solution is unbounded in the worst case.     

Finite-production-rate inventory models with first-and second-shift setups

This article considers the production planning problem of a shop which can produce in either one shift or two shifts. Setup cost is charged whenever there is an increase in the production rate from one period to the next. Efficient planning horizon procedures have been developed for this model. A numerical example has been included to illustrate the planning horizon results.     

Planning horizon procedures for machine replacement models with several possible replacement alternatives

This paper develops a forward algorithm and planning horizon procedures for an important machine replacement model where it is assumed that the technological environment is improving over time and that the machine-in-use can be replaced by any of the several different kinds of machines available at that time. The set of replacement alternatives may include (i) new machines with different types of technologies such as labor- and capital- intensive, (ii) used machines, (iii) repairs and/or improvements which affect the performance characteristics of the existing machine, and so forth. The forward dynamic programming algorithm in the paper can be used to solve a finite horizon problem. The planning horizon results give a procedure to identify the forecast horizon T such that the optimal replacement decision for the first machine based on the forecast of machine technology until period T remains optimal for any problem with horizon longer than T and, for that matter, for the infinite horizon problem. A flow chart and a numerical example have been included to illustrate the algorithm.     

A note on integer linear fractional programming

This note consists of developing a method for enforcing additional constraints to linear fractional programs and showing its usefulness in solving integer linear fractional programs.     

A parallel machine replacement model

This paper considers a finite horizon parallel machine replacement problem where a fixed number of machines is in operation at all times. The operating cost for a machine goes up as the machine gets older. An older machine may have to be replaced by a new one when its operating cost becomes too high. There is a fixed order cost associated with the purchase of new machines. Machine purchase prices and salvage values may depend on the period in which they were purchased. The objective is to find a replacement plan that minimizes the total discounted cost over the problem horizon. We believe that the costs in our model are more commonly observed in practice than those previously used in the literature. The paper develops properties of optimal solutions and an efficient forward‐time algorithm to find an optimal replacement plan. A dominance property is developed that further limits the options to be considered, and a simple forecast horizon result is also presented. Future research possibilities are mentioned. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 275–287, 2002; Published online in Wiley InterScience (http://www.interscience.wiley.com). DOI 10.1002/nav.10012     

OPTIMAL FACILITY LOCATION UNDER RANDOM DEMAND WITH GENERAL COST STRUCTURE

This paper investigates the problem of determining the optimal location of plants, and their respective production and distribution levels, in order to meet demand at a finite number of centers. The possible locations of plants are restricted to a finite set of sites, and the demands are allowed to be random. The cost structure of operating a plant is dependent on its location and is assumed to be a piecewise linear function of the production level, though not necessarily concave or convex. The paper is organized in three parts. In the first part, a branch and bound procedure for the general piecewise linear cost problem is presented, assuming that the demand is known. In the second part, a solution procedure is presented for the case when the demand is random, assuming a linear cost of production. Finally, in the third part, a solution procedure is presented for the general problem utilizing the results of the earlier parts. Certain extensions, such as capacity expansion or reduction at existing plants, and geopolitical configuration constraints can be easily incorporated within this framework.     

Should firms conceal information when dealing with common suppliers?

A firm making quantity decision under uncertainty loses profit if its private information is leaked to competitors. Outsourcing increases this risk as a third party supplier may leak information for its own benefit. The firm may choose to conceal information from the competitors by entering in a confidentiality agreement with the supplier. This, however, diminishes the firm's ability to dampen competition by signaling a higher quantity commitment. We examine this trade‐off in a stylized supply chain in which two firms, endowed with private demand information, order sequentially from a common supplier, and engage in differentiated quantity competition. In our model, the supplier can set different wholesale prices for firms, and the second‐mover firm could be better informed. Contrary to what is expected, information concealment is not always beneficial to the first mover. We characterize conditions under which the first mover firm will not prefer concealing information. We show that this depends on the relative informativeness of the second mover and is moderated by competition intensity. We examine the supplier's incentive in participating in information concealment, and develop a contract that enables it for wider set of parameter values. We extend our analysis to examine firms' incentive to improve information. © 2014 Wiley Periodicals, Inc. 62:1–15, 2015     

Scheduling of parallel processors: A posterior bound on LPT sequencing and a two-step algorithm

This article considers the problem of scheduling parallel processors to minimize the makespan. The article makes two key contributions: (1) It develops a new lower bound on the makespan for an optimal schedule, and (2) it proposes an efficient two-step algorithm to find schedules of any desired accuracy, or percent above optimal. In addition, a posterior bound on LPT (longest processing time) sequencing is developed in the article. It is proved that this bound dominates the previously reported bounds on LPT sequencing.