Xiaoqiang Cai

A genetic algorithm for scheduling staff of mixed skills under multi-criteria

Abstract We consider the problem of scheduling staff with mixed skills. We formulate the problem as a multi-criteria optimization model, where the primary objective is to minimize the total cost for assigning staff to meet the manpower demands over time, the secondary objective is to seek a solution with the maximum surplus of staff among the solutions with almost same level of assigning cost, and the tertiary objective is to reduce the variation of staff surplus over different scheduling periods. This is a new model to handle the staff scheduling problem, which is motivated by the operational requirements in some local service organizations. We propose a new genetic algorithm (GA) to solve the problem. The proposed GA differs from traditional GAs in the following components: (1) it performs its parent selection by using a ranking scheme that considers successively the three criteria; (2) it uses a multi-point crossover operator based on the hamming distance between schedules; and (3) it adopts a heuristic to resolve the problem of infeasibility created by crossover operations. Computational results are reported, which show the effectiveness of the proposed approach in finding desirable solutions.

Scheduling with multiple-job-on-one-processor pattern

Most scheduling literature considers a “one-job-on-one-processor” pattern, which assumes that a processor processes exactly one job at a time. In this paper we consider a new scheduling problem with a “multiple-job-on-one-processor” pattern, where several jobs can be processed by a single processor simultaneously, provided that the total size of the jobs being processed does not exceed the capacity of the processor at any point in time. This problem is motivated by the operation of berth allocation, which is to allocate vessels (jobs) to a berth (processor), where the vessels, if small in dimension, may share the berth with some other vessels for loading/unloading the goods. We consider the problem to minimize the makespan of the schedule. The well-known First-Fit Decreasing heuristic is generalized and applied to several variations of the problem, and the worst-case behavior of the generalized heuristics is studied. Worst-case error bounds are obtained for those models. Computational experiments are cond...

Uncapacitated production planning with multiple product types, returned product remanufacturing, and demand substitution

This paper investigates an uncapacitated multi-product production planning problem with returned product remanufacturing and demand substitution, where no backlog and no disposal are allowed. Both the production of new products and the remanufacturing of returned products are considered to meet time-varying demands in a finite time horizon. Setup costs are taken into account when a new product is manufactured or a returned product is remanufactured. The problem is to determine when and how many returned products are remanufactured and new products are manufactured so as to minimize the total cost, including manufacturing, remanufacturing, holding and substitution costs. We first develop an optimization model to formulate the problem. We then propose a dynamic programming approach to derive the optimal solution in the case with large quantities of returned products. We further propose an approximate approach for the general problem to compute a near-optimal solution. The proposed approaches are evaluated by computational experiments and the effectiveness of the approximate approach is verified. Some managerial insights regarding the effects of remanufacturing/substitution are also obtained from the computational studies.

Time‐varying shortest path problems with constraints

We study a new version of the shortest path problem. Let G = (V, E) be a directed graph. Each are e ∈ E has two numbers attached to it: a transit time b(e, u) and a cost c(e, u), which are functions of the departure time u at the beginning vertex of the arc. Moreover, postponement of departure (i.e., waiting) at a vertex may be allowed. The problem is to find the shortest path, i.e., the path with the least possible cost, subject to the constraint that the total traverse time is at most some number T. Three variants of the problem are examined. In the first one, we assume arbitrary waiting times, where waiting at a vertex without any restriction is allowed. In the second variant, we assume zero waiting times, namely, waiting at any vertex is strictly prohibited. Finally, we consider the general case whre there is a vertex-dependent upper bound on the waiting time at each vertex. Several algorithms with pseudopolynomial time complexity are proposed to optimally solve the problems. First, we assume that all transit times b(e, u) are positive integers. In the last section, we show how to include zero transit times.

Optimal acquisition and production policy in a hybrid manufacturing/remanufacturing system with core acquisition at different quality levels

We study the acquisition and production planning problem for a hybrid manufacturing/remanufacturing system with core acquisition at two (high and low) quality conditions. We model the problem as a stochastic dynamic programming, derive the optimal dynamic acquisition pricing and production policy, and analyze the influences of system parameters on the acquisition prices and production quantities. The production cost differences among remanufacturing high- and low-quality cores and manufacturing new products are found to be critical for the optimal production and acquisition pricing policy: the acquisition price of high-quality cores is increasing in manufacturing and remanufacturing cost differences, while the acquisition price of low-quality cores is decreasing in the remanufacturing cost difference between high- and low-quality cores and increasing in manufacturing and remanufacturing cost differences; the optimal remanufacturing/manufacturing policy follows a base-on-stock pattern, which is characterized by some crucial parameters dependent on these cost differences.

Double marginalization and coordination in the supply chain with uncertain supply

This paper explores a generalized supply chain model subject to supply uncertainty after the supplier chooses the production input level. Decentralized systems under wholesale price contracts are investigated, with double marginalization effects shown to lead to supply insufficiencies, in the cases of both deterministic and random demands. We then design coordination contracts for each case and find that an accept-all type of contract is required to coordinate the supply chain with random demand, which is a much more complicated situation than that with deterministic demand. Examples are provided to illustrate the application of our findings to specific industrial domains. Moreover, our coordination mechanisms are shown to be applicable to the multi-supplier situation, which fills the research gap on assembly system coordination with random yield and random demand under a voluntary compliance regime.

Remanufacturing and pricing decisions with random yield and random demand

Remanufacturing is creating considerable benefit to industry and community, but the uncertainties in both supply and demand sides bring significant difficulty to the production and marketing management of remanufactured products. This paper considers the remanufacturing and pricing decisions when both the remanufacturing yield and the demand for remanufactured products are random. Two typical sequential decision strategies are explored: First-Remanufacturing-Then-Pricing (FRTP) and First-Pricing-Then-Remanufacturing (FPTR). The optimal remanufacturing quantity and selling price of the remanufactured product are developed for each strategy, under negligible salvage value and shortage penalty. We also conduct a numerical study to investigate the scenario where the salvage value and shortage penalty are non-negligible, and explore the parameter sensitivity of the systems. We find that FRTP strategy is more preferable for low remanufacturing cost, market-price sensitivity, and variance of demand randomness, and for high shortage penalty, salvage value, and variance of remanufacturing yield; while FRTP strategy is more preferable for the complementary situation.

Optimal on-line algorithms for scheduling on parallel batch processing machines

We consider the problem of scheduling jobs on-line on parallel batch processing machines with dynamic job arrivals to minimize makespan. We are given m identical batch processing machines, each of which can handle up to B (the capacity of a machine) jobs simultaneously. The jobs that are processed together form a batch, and all jobs in a batch start and complete at the same time. The processing time of a batch is a constant, which is independent of the number and identity of the jobs. Each job becomes available at its arrival time, which is unknown in advance. First we deal with the unbounded case where the capacity of the batch processing machines is infinite, and derive an optimal on-line algorithm with competitive ratio 1+ g m , where g m >0 is determined by (1+ g m ) m +1 = g m +2. We then consider the bounded case where the capacity B of the batch processing machines is bounded. We provide an on-line algorithm with competitive ratio (\sqrt{5}+1)/2 (the golden ratio) and prove that the result is the best possible for all m .

Scheduling jobs with random processing times on a single machine subject to stochastic breakdowns to minimize early‐tardy penalties

We examine the problem of scheduling n jobs with a common due date on a single machine. The processing time of each job is a random variable, which follows an arbitrary distribution with a known mean and a known variance. The machine is not reliable; it is subject to stochastic breakdowns. The objective is to minimize the expected sum of squared deviations of job completion times from the due date. Two versions of the problem are addressed. In the first one the due date is a given constant, whereas in the second one the due date is a decision variable. In each case, a general form of the deterministic equivalent of the stochastic scheduling problem is obtained when the counting process related to the machine uptime distribution is a generalized Poisson process. A sufficient condition is derived under which optimal sequences are V-shaped with respect to mean processing times. Other characterizations of optimal solutions are also established. Based on the optimality properties, algorithms with pseudopolynomial time complexity are proposed to solve both versions of the problem.

The Value of Processing Flexibility in Multipurpose Machines

We study a scheduling problem in a multipurpose machine environment where every job can be processed by a subset of the machines operated in parallel, with the objective of minimizing makespan. We develop lower bounds, heuristic algorithms, and a branch-and-bound procedure. We perform an extensive computational experiment to assess how much flexibility is enough to render the multipurpose machine system equally efficient to an equivalent system of parallel identical machines. We find that very small amounts of flexibility appropriately distributed across processors provide nearly the same makespan performance as a system of fully flexible parallel machines.