Asia-Pacific Journal of Operational Research

The note deals with machine scheduling problems with a more general learning effect model, i.e., the actual job processing time is a function of the sum of the function of the processing times of the jobs already processed and job position. We show that some single machine scheduling problems are still polynomially solvable under the proposed model. We also show that some special cases of the flow shop scheduling problems can be solved in polynomial time.

Job learning and deterioration coexist in many realistic machine-job scheduling situations. However, in literature, the constructed forms of the machine scheduling models with job learning and/or deteriorating effects were specific types of functions, which constrained their applicability in practice. This paper introduces a new single-machine scheduling model, where the actual processing time of a job is a general function of its starting time as well as scheduled position, which shows a broad generalization in contrast to that of certain existing models. For three objectives corresponding to the single-machine scheduling problem–total weighted completion time, discounted total weighted completion time, and maximum lateness — this paper presents their respective approximation result on the basis of the worst-case bound analysis from the optimal algorithm. The results demonstrate that under our proposed model, minimization of scheduling operations such as the makespan, sum of the kth power of completion times, and total lateness are polynomially solvable. Moreover, under some feasible conditions for the scheduling parameters, the minimum optimization problems of the total weighted completion time, discounted total weighted completion time, maximum lateness, and total tardiness are all recognized as polynomial forms and their solutions are provided.

We study an optimal inventory control and allocation for a seller who uses sequential Internet auctions to sell replenishment products. This problem is faced not only by retailers/distributors in the retail industry but also by manufacturers who use sequential Internet auctions to sell products that can be replenished. We consider the total expected discounted profit criterion in a finite horizon and both the discounted and average profit criteria over an infinite horizon, and show the optimality of the so-called base-stock-allocate-all (BSAA) policies. Then, we simplify the problem of computing the optimal policies and profits for either the discounted or average profit criterion in an infinite horizon to an optimization problem with only one integer decision variable. We show these results for the list price case, and also for the case where the reserve price is a decision variable. Finally, numerical results are given, where the effects of several model parameters on the optimal policies and profits are numerically analyzed.

In this paper, a revenue sharing contract is designed to coordinate a distribution channel where the demand of the product is ramp-type price and effort sensitive. It is shown that traditional revenue sharing contract does not coordinate the system. As an alternative, two new mechanisms are proposed (i) revenue sharing with coordinated effort of the retailer alone and (ii) both revenue and effort sharing contract. In addition, a crucial modification of revenue sharing fraction is also proposed. To enhance the applicability of revenue sharing contract, the contract parameters are determined by using bi-level multi-objective fuzzy goal programming technique where manufacturer sets the wholesale price greater than the marginal cost. Numerical examples are presented to illustrate all the models.

Although many researches have conjectured the optimality of the hedging point policy for the multiple-product stochastic capacitated periodic review problem, it is still a challenge to prove the hypothesis. This paper considers a special case of the capacitated multiple-product periodic review problem where stochastic demand distribution, production rate, unit production cost and periodic expected inventory cost are the same for all different products. For this symmetric problem, we prove an optimal policy where ordering and non-ordering regions for every product are defined. Our research provides significant implications to the characterization of the optimal policy for the general problem.

We focus our research on a supply chain involving one buyer and two independent suppliers of the same product. The main supplier is prone to supply disruption and recurrent supply uncertainty, and the backup supplier is perfectly reliable but supply goods at higher prices. Three kinds of backup contracts between the buyer and the backup supplier are investigated to mitigate supply risks: A capacity reservation contract, a make-to-order contract, and a buy-back contract. Models are developed to study how the buyer's expected profit and optimal decisions related to each contract change with the supply risks. We also examine the sensitivity of various cost parameters on the optimal decisions, and compare the values of three backup contracts for the buyer. Furthermore, we present how these results differ from those obtained in the analysis with demand uncertainty considered. Our study provides managerial insights into the positive effects of different backup contracts on the buyer's expected profit in the events of unexpected disruption.

One crucial matter in routine life is decision-making. Although decision-making in everyday life appears to be easily dealt with by one-on-one comparisons, the same is not true with decision-making in business. In business management decisions, problems are more complicated than those in individual life because most business situations fall into the category of multi-criteria decision-making (MCDM) problems. Therefore, appropriate multi-criteria decision methods should be carefully selected to solve these problems. This study uses the analytic network process (ANP), one of the widely available multi-criteria decision methods. However, this popular method generally ignores the uncertainty inherent in the input data. Therefore, this paper proposes an improved process that considers uncertainty by using Monte Carlo analysis with input values then applied to the ANP procedures. This proposed method is implemented by a real business that produces roof tiles; the primary goal of the study is to select among newly developed roof formulas by considering the uncertainty and interrelation among decision criteria and elements as well as alternatives. The outcomes of study accurately rank the new product formulas. Furthermore, the results of improved method differ the rankings produced by the original ANP. The observed dissimilarities mainly result from uncertainty consideration discussed in this study.

In many settings, systems are composed of a group of independent sub-units. Each sub-unit produces the same set of outputs by consuming the same set of inputs. Conventional data envelopment analysis (DEA) views such a system as a "black-box", and uses the sum of the respective inputs and outputs of all relevant component units to calculate the system efficiency. Various DEA-based models have been developed for decomposing the overall efficiency. This paper further investigates this kind of structure by using the cooperative (or centralized) and non-cooperative (Stackelberg or leader–follower) game theory concepts. We show that the existing DEA approaches can be viewed as a centralized model that optimizes the efficiency scores of all sub-units jointly. The proposed leader–follower model will be useful when the priority sequence is available for sub-units. Consider, for example, the evaluation of relative efficiencies of a set of manufacturing facilities where multiple work shifts are operating. Management may wish to determine not only the overall plant efficiency, but as well, the performance of each shift in some priority sequence. The relationship between the system efficiency and component efficiencies is also explored. Our approaches are demonstrated with an example whose data set involves the national forests of Taiwan.

A single-level optimization model (i.e., a Route Flow Estimator (RFE)) has been proposed to estimate the historical air travel demand. However, the RFE may require a significant amount of additional data collection effort when applied to estimate travel demand in small or medium-sized networks. We propose a novel bi-level model as an alternative to the RFE to handle demand estimation for small or medium-sized networks. The upper-level model is designed as a constrained least square (LS) model. The lower-level model is designed based on the RFE. The bi-level model estimates travel demand by considering travelers' choice behaviors and some observed data. It requires less data collection effort yet it produces estimation results consistent with those from the RFE. A Gauss–Seidel type (GST) algorithm is proposed to solve the bi-level model. To solve the upper-level model, we propose a heuristic algorithm, which is designed to solve the dual of the upper-level model. The estimation results from the two models are compared using two numerical examples: a small-sized example with one OD pair and a medium-sized example with 400 OD pairs.

An unpredictable breakdown often occurs and tends to complicate production scheduling in a steelmaking-continuous casting (SCC) plant. Because of particular characteristics and technology constraints of the SCC plant, traditional robust scheduling often provides an excessively conservative solution. This paper proposes an effective proactive scheduling that utilizes robustness adopting a distribution curve of a system performance created as a mix-integer model. The proposed robustness is designed to work effectively with the existing factory operation and is based on uncertainty assessment. In this paper, artificial neural network (ANN) is adopted with a challenge of designing an accurate model due to the model complexity from the discrete and nonlinear properties of the system performance. The ANN model is achieved by applying k-mean clustering, which decomposes machines to smaller groups having similar effect to the uncertainty. A case study based on data from a real SCC plant is conducted to demonstrate the methodology. The experimental result shows that the proposed methodology is successful in designing a robust schedule that provides a lower production cost under an acceptable breakdown probability while also consuming less computational time compared with the traditional approach.