برنامه ریزی هماهنگ مراحل تولید و تحویل با هزینه های برگزاری موجودی وابسته به مرحله

This paper considers a problem of integrated decision-making for job scheduling and delivery batching wherein different inventory holding costs between production and delivery stages are allowed. In the problem, jobs are processed on a facility at a production stage and then delivered at the subsequent delivery stage by a capacitated vehicle. The objective is to find the coordinated schedule of production and delivery that minimizes the total cost of the associated WIP inventory, finished product inventory and delivery, where both the inventory costs are characterized in terms of the weighted flow-time and the delivery cost is proportional to the required number of delivery batches. It is proved that the problem is NP-hard in the strong sense. Thereupon, three heuristic algorithms are derived. Some restricted cases are also characterized as being solvable in polynomial time. Numerical experiments are conducted to evaluate the performance of the derived heuristic algorithms.

This paper considers a problem of integrated decision-making for job scheduling and delivery batching wherein different (stage-dependent) inventory holding costs between production and delivery stages are allowed. In the problem, jobs are processed on a production facility and then delivered to a customer by a capacitated vehicle. The customer can be interpreted as a distribution center (or, warehouse). Therefore, all the completed jobs from the production facility are frequently delivered in batches to the distribution center. The objective is to find the coordinated schedule of production and delivery that minimizes the total cost of the associated inventory and delivery. The inventory cost is generally computed by the multiplication of the unit holding cost and the flow-time spent in the system. The holding cost represents a combination of the cost of capital, the cost of physical storage and the cost of losses due to spoilage; hence, it highly depends on the inventory type (or value). Therefore, this paper explicitly distinguishes between two types of inventory cost. The first is incurred by WIP (work-in-process) and the second is incurred by finished product. To compute the inventory costs, this paper incorporates two types of flow-time: production flow-time and delivery flow-time. The production flow-time of each job represents the time until the processing of the job is completed. The WIP-inventory cost is assumed to be proportional to the production flow-time. The finished jobs are stored and then delivered to the customer. Therefore, the delivery flow-time of each job can be measured by the time that lapses from the completion of production to the completion of delivery. It is noted that delivery is commonly made in batches subject to a given vehicle capacity so that the delivery flow-time of each job depends on the associated delivery schedule. The finished-product inventory cost is incurred during the delivery flow-time. Thus, the overall inventory cost is measured by the weighted sum of the two flow-times, where the weights are represented by their respective unit holding costs. Moreover, the delivery cost is modeled to be proportional to the number of deliveries that are to be made for all the jobs. In the literature, much research has focused on the area of integrating job scheduling and delivery batching together, under various assumptions and objective measures that differ from the problem proposed in this paper. For example, Potts [1] and Hall and Shmoys [2] have studied scheduling problems with non-identical job-release times and delivery times, under the assumption that a sufficient number of vehicles are available to deliver the jobs. Lee and Chen [3], Sung and Kim [4] and [5], Chang and Lee [6] and Li et al. [7] considered capacity restrictions on delivery batches, but tried to only minimize some scheduling objectives, without considering any delivery costs, including the makespan, the sum of completion times, the maximum lateness, the number of tardy jobs and the total tardiness. Pundoor and Chen [8] considered the maximum tardiness and delivery cost together. Lee and Chen [3], Sung and Kim [4] and [5], Pundoor and Chen [8] and Li et al. [7] considered the situation of identical job-sizes, but Chang and Lee [6] considered the case where job-sizes varied. Yang [9] and Hall et al. [10] analyzed various production-and-delivery scheduling problems with fixed batch-delivery time-points, under the assumptions of infinite vehicle capacities, a sufficient number of vehicles and no delivery costs. Herrmann and Lee [11], Yuan [12], Chen [13], Cheng et al. [14], Hall and Potts [15], Lin et al. [16], Yan and Tang [17] and Day et al. [18] analyzed various machine-scheduling problems for jobs to be delivered in batches following job-processing, under the assumption of infinite vehicle capacities but with a charge for delivery. Qi [19] considered a situation where the raw material for processing jobs is delivered in batches to a single machine and the raw material delivery and job sequencing decisions are made simultaneously. He derived a branch-and-bound algorithm to minimize the sum of the delivery and flow-time costs. Chen [20] has published a recent review of the research on production-and-delivery scheduling problems. All the above cited references assumed that the inventory holding costs per unit-time at the production and delivery stages are the same. However, the inventory holding cost per unit-time of each finished product is greater than that of any intermediate product, which suggests that it may be appropriate to model the inventory holding cost as being stage-dependent. Stage-dependent inventory holding costs are expected to make the coordination between production and delivery more effective. The organization of this paper is as follows. Section 2 describes the problem. 3 and 4 characterize some solution properties, upon which three heuristic algorithms are derived. Some numerical experiments are conducted to evaluate the performance of the derived heuristic algorithms. Some restricted cases are also characterized as being solvable in polynomial time. Section 5 makes some concluding remarks.

This paper considers a coordinated production-and-delivery scheduling problem that incorporates stage-dependent (WIP vs. finished-goods) inventory holding costs. At the outset, the problem is shown to be NP-hard in the strong sense. Correspondingly, three heuristic algorithms are developed and tested for their ability to find good solutions within a reasonable time. Moreover, several restricted cases are also characterized as being solvable in polynomial time. The results of this paper can be only applied to certain limited situations, wherein production is executed by only one machine and finished products are delivered to only one site by only one vehicle. Nevertheless, to the best of our knowledge, this paper represents the first attempt that allows differential holding costs that depend on the value of materials. Hence, the results may provide the basis for further studies of multiple-machine shops, such as flowshops and multiple-site and multiple-vehicle scheduling problems.