Asia-Pacific Journal of Operational Research

In this paper an inventory control system for deteriorating items with price and time-dependent demand is studied. The majority of the existing literature in inventory systems for deteriorating items, deals with items that are subject to deterioration as soon as they enter the warehouse. However, there are items that have a shelf-life and start deteriorating after a time lag (noninstantaneous deteriorating items). Under some special circumstances, i.e., attractive price discount, low storage cost, high demand, etc; the procurement of a large amount of such items at a time is decided. Because of the fixed capacity of the own warehouse (OW), a rented warehouse (RW) is used to store the excess quantity. In the present paper, a two-warehouse inventory model for noninstantaneous deteriorating items is developed. Shortages at OW are also allowed and partially backlogged at a rate, which is any nonincreasing function of the waiting time up to the next replenishment. For this model, we propose a simple solution procedure to determine the optimal pricing and replenishment schedule.

In this paper, we develop a real options framework that sets rules for investment decision in sustainable transport projects under both demand and costs uncertainties. First, we present the model we use to calculate the cost of transport externalities. Using stochastic analysis, we show how to maximize inter-generational utility by choosing the optimal time to invest. The method is implemented using a dynamic programming approach that gives, at each moment, the thresholds for demand and cost for which it is optimal to invest. We calculate the expected waiting time until investing and perform a sensitivity analysis to study the impact of the different parameters on the decision.

Many multi-state systems settle on more than one operating levels and the elementary states having a common operating level can be treated as one. In this paper, one kind of such Markov repairable systems is introduced, which is named aggregated Markov repairable systems with multi-operating levels. In the system, the functioning states are lumped together according to their membership as a common operating level and each operating level is characterized by a performance rate. The systems degrade from a higher operating level to a lower one when no preventive maintenances (PMs) are performed. While the system is in some deteriorated operating levels that are easy to be recognized PMs are carried out. The PMs may be perfect or imperfect. If the system fails, the repairs may restore it to any of its operating levels. A multivariate semi-Markov process is build to describe performance properties of the system. Several reliability indices such as the availability, frequencies of repairs and failures are presented. Furthermore, the up time, the length of a cycle, the sojourn times in various operating levels and visiting numbers to them, the times that the system satisfies demands of customers and the output during a cycle are studied. Semi-Markov process theory, Laplace transform and matrix methods are employed in the study. A numerical example is given to illustrate the results in the paper. The impact of PM on the system is considered through the numerical illustration.

This paper develops a novel mixed integer nonlinear programming model for the intra-cell layout design of dynamic cellular manufacturing systems. In dynamic environment, the product mix and part demand are varying during a multi-period planning horizon. As a result, the cell configuration for one period may not be efficient for successive periods and thus necessitates reconfigurations. The proposed model incorporates several design features including intra-cell layout, operation sequence, operation time, alternative process routings, duplicate machines, purchase machine, machine capacity, route selection, production volume of parts, part movements in batch and cell reconfiguration. By considering intra-cell layout and operation sequence, the material handling volume and related cost is calculated more exactly. The objective is to minimize the total costs of inter-cell material handling, forward and backward intra-cell material handling, setting up route, machine relocation, purchasing new machines, machine overhead and machine processing. The main constraints are route selection among flexible routings, machine availability, cell size, machine time-capacity and machine location. The proposed model cannot be solved for large-sized problems optimally within a reasonable amount of computational time. Therefore, an efficient simulated annealing algorithm is developed to overcome NP-hardness of the proposed model.

A multilinear extension of the n-person cooperative game was introduced by Owen in 1972, and a new extension method is proposed in this paper. For n-person cooperative games, any coalition can equivalently be represented by its characteristic vectors. By means of the Choquet integral, a new fuzzy extension, called the Choquet extension, is developed. Furthermore, a Shapley function in this class of fuzzy cooperative games with the Choquet extension form is defined. Axioms of the Shapley function are proposed, and an explicit formula for the Shapley function is given. Finally, an equivalent definition of this Shapley function is discussed.

This study investigated railway line planning optimization models that determine the frequency of trains on each line to satisfy passenger origin–destination demands while minimizing related costs. Most line planning models assume that all trains on the same route run with the same halting pattern. However, to minimize passenger travel time and to provide a train service with faster travel times to as many stations as possible, we must consider various halting patterns; these patterns can be provided in advance or are required to be formulated. Our study addresses two line planning problems that consider halting patterns, describes the computational complexities of each problem, and presents the column generation approach for one model. We also present experimental results obtained for the Korean high-speed railway network.

We look at a Cournot model in which each firm may be unreliable with random capacity, so the total quantity brought into market is uncertain. The Cournot model has a unique pure strategy Nash equilibrium (NE), in which the number of active firms is determined by each firm's production cost and reliability. Our results indicate the following effects of unreliability: the number of active firms in the NE is more than that each firm is completely reliable and the expected total quantity brought into market is less than that each firm is completely reliable. Whether a given firm joins in the game is independent of its reliability, but any given firm always hopes that the less-expensive firms' capacities are random and stochastically smaller.

Cross evaluation matrix was suggested to resolve a ranking problem in the data envelopment analysis (DEA) context. The cross evaluation matrix is composed of simple efficiency and cross-efficiency (CE) values of decision making units (DMUs). However, simple efficiency cannot discriminate efficient DMUs because of the nature of basic DEA models. To make complete use of the efficiency information of DMUs, a modified cross evaluation matrix is proposed. The modified matrix consists of super-efficiency (SE) values for diagonal elements and CE values for nondiagonal elements. As the efficiency values are not limited to "1" in SE approach, the proposed matrix can explain the difference of efficiency of efficient DMUs. The proposed matrix can be more accurate than the original cross evaluation matrix. Consequently, the rank order of DMUs generated by the suggested matrix reflects differences in relative efficiency of DMUs. A numerical example is given to show the superiority of the proposed approach. This is done by comparing with other available ranking methods in the DEA context. Several distance measures are utilized to compare rank consistency of the ranking methods. Finally, a case study is presented to explain how our approach is applied to real ranking problems.

In this paper, we extend Lin [Lin, YJ (2008). Minimax distribution free procedure with backorder price discount. International Journal of Production Economics, 111, 118–128] model by fuzzifying the demand rate, based on triangular fuzzy number to increase its applicability and solve the problem by using an alternative approach i.e., Chebyshev approach. We prove the concavity and convexity of the estimate of total variable cost per unit time in fuzzy sense. To compare the expected annual cost of proposed model, defuzzification is performed by two different methods namely signed distance and centroid method. We provide a solution procedure to find the optimal values of lead-time, the order quantity and the backorder price discount by using minimax distribution free procedure and Chebyshev approach. Through numerical example it is shown that there is a significant saving in cost due to crashing cost to reduce the lead-time and the setup cost. We also compare our results with Cheng et al. [Cheng, TL, CK Huang and KC Chen (2004). Inventory model involving lead-time and setup cost as decision variables. Journal of Statistics and Management Systems, 7, 131–141] model and show that Ben-Daya and Raouf's [Ben-Daya, M and A Raouf (1994). Inventory model involving lead-time as a decision variable. Journal of the Operational Research Society, 45, 579–582] model is the special case of our proposed model.

Tabu search (TS) has always been a very popular algorithm for graph coloring, both as a stand-alone optimizer as well as a subroutine inside population-based hybrid methods. We present two TS extensions that could allow previous TS algorithms to improve their behavior at almost no additional computational cost. First, we integrate two new evaluation functions which employ supplementary (structural or dynamic) information in addition to the conventional objective function (the number of edges with both ends of the same color). These new evaluation functions allow the search process to differentiate configurations not distinguished by the conventional evaluation function. The second extension concerns a reactive mechanism for improving the tabu list management. Theoretical arguments show that this reactive component completely eliminates the risk of getting blocked looping on plateaus. Numerical experiments show that the two proposed TS extensions can be very useful inside a stand-alone TS optimizer, as well as inside TS subroutines of state-of-the-art hybrid methods.