Asia-Pacific Journal of Operational Research

In this paper, single-machine scheduling problems with proportional linear deterioration effects and common due window assignment simultaneously are considered. Two different objective functions are studied, the first is to minimize the sum of the number of early jobs, number of tardy jobs and due window location and due window size, the second is to minimize the sum of the earliness cost, tardiness cost, due window location and due window size. Optimality properties for all problems are provided and polynomial time algorithms for solving these problems are given.

We consider a two-machine flow shop scheduling with two properties. The first is that each due date is assigned for a specific position different from the traditional definition of due dates, and the second is that a consistent pattern exists in the processing times within each job and each machine. The objective is to minimize maximum tardiness, total tardiness, or total number of tardy jobs. We prove the strong NP-hardness and inapproximability, and investigate some polynomially solvable cases. Finally, we develop heuristics and verify their performances through numerical experiments.

In this paper, we consider two single machine scheduling problems with outsourcing under different fill rates or quantity discount rates. From the manufacturer point of view, to maintain a predefined high service level under limited production capacity, it is required that the number of outsourced jobs must belong to a given interval $[a,b]$. We call this model “scheduling with outsourcing under different fill rates”. Meanwhile, from the outsourcers point of view, in order to encourage more outsourcing actions from the manufacturer, the outsourcers might provide an attractive discount scheme. Here, we assume that all discount rates depend only on the quantity (number) of the outsourced jobs. That is, the actual outsourcing cost equals to the original outsourcing cost multiplied by the corresponding discount rate. This model is called “scheduling with outsourcing under different quantity discount rates”. The objective is to minimize the sum of the makespan of the processed jobs and the (actual) outsourcing costs of the outsourced jobs. For the above two problems, some optimal algorithms, approximation algorithms and approximation schemes are proposed.

In this note, we introduce a new finite difference approximation called the Black-Box Logarithmic Expansion Numerical Derivative (BLEND) algorithm, which is based on a formal logarithmic expansion of the differentiation operator. BLEND capitalizes on parallelization and provides derivative approximations of arbitrary precision, i.e., our analysis can be used to determine the number of terms in the series expansion to guarantee a specified number of decimal places of accuracy. Furthermore, in the vector setting, the complexity of the resulting directional derivative is independent of the dimension of the parameter.

We consider a first-price sealed-bid procurement auction between two capacity constrained bidders. Either bidder, due to the capacity constraint, is unable to fulfill the auctioned project from a buyer. We consider two formats of capacity cooperation between the two competing bidders: ex ante subcontracting and ex post subcontracting. In the former case, two bidders first bargain over the capacity cooperation contract and then compete with each other by bidding for the buyer’s project. In the latter case, two bidders first submit bids to the buyer and then bargain over the capacity cooperation contract. With ex ante or ex post subcontracting, two bidders have the so-called co-opetition relationship: they compete to win the auction but cooperate through subcontracting. We find that bidders’ subcontract timing has a fundamental impact on their competitive bidding behavior and profits. Both bidders will benefit from the ex ante subcontracting, and submit higher equilibrium bid prices, compared to the case without subcontracting. The ex post subcontracting, however, will lower the equilibrium bid price and may hurt the bidder with capacity advantage when bidders’ relative bargaining power is not consistent with the relative capacity advantage.

Among homogeneous entities, there are some shared resources from which all the entities benefit. A significant point is to allocate the fixed costs of these shared resources equitably between entities. Data envelopment analysis is a technique applied for decision-making, concerning and evaluating the performance of decision-making units. One of the functions of these units is to solve the fair fixed cost allocation problem, based on the performance of a set of homogeneous decision-making units. In this paper, a method for allocating fixed costs using cross efficiency has been suggested, where the obtained result is Pareto cross-efficient. Moreover, the proposed method helps estimate the value of $𝜀$ (lower bound of weights) and the mode of selecting $𝜀$ for the suggested model using the standard deviation. Finally, by using a numerical example, the proposed method of allocating fixed costs is compared to the previous ones.

The manager is responsible for the operations of a distribution center (DC) and multiple retail outlets selling a seasonal product. Initially, the DC keeps the inventory, which is allocated to the outlets in the season. There are inventory holding costs at the DC and the outlets; variable shipment cost for transferring inventory from the DC; fixed ordering cost and shortage cost at an outlet. Exact demand at each outlet is a decreasing function of price. To maximize the expected profit of the season, the manager needs to determine the markdown prices for retail outlets and quantity of inventory allocated to them. The problem can be modeled as a dynamic program (DP) which takes too heavy computational effort to solve. We develop a DP-based heuristic for solving the problem. The heuristic takes light computational effort and yet has good accuracy. Insights streamlining the markdown operations are deduced from the numerical results.

We consider a class of variational inequality problems with linear constraints, where the mapping is unknown and the system is an oracle. The capacitated traffic congestion pricing problem of transportation is such an application, and many classical methods cannot deal with this class of problems. Note that the cost of the observation (observe the exact solution of the subproblem) is very expensive. It is important to get an inexact solution instead of an exact solution, especially when the iteration is far from the solution set. In this paper, we propose a modified inexact prediction–correction method. Under the mild condition that the underlying mapping is strongly monotone, we prove the global convergence. Some numerical examples are presented to illustrate the efficiency of the inexact strategy.