A note on special optimal batching structures to minimize total weighted completion time

A batch is a subset of jobs which must be processed jointly in either serial or parallel form. The algorithmic aspects of the batching scheduling problems have been extensively studied in the literature. This paper presents necessary and sufficient conditions of the existence of optimal batch sequences for the single machine, batching, total weighted completion time scheduling problems on two batching ways: (1) all jobs form one batch; (2) each batch contains a single job. This kind of conditions can help us to recognize some special optimal schedules quickly. Research supported by NSFC (10671183).     

Decision support system for the batching problems of steelmaking and continuous-casting production

This paper investigates two batching problems for steelmaking and continuous-casting (SCC) production in an integrated iron and steel enterprise. The tasks of the problems are to make the decisions as how to consolidate ordered slabs into charges, and then how to group charges into casts. The effective decisions on these batching problems can help to balance the requirements of materials in downstream production lines, improve the customer satisfaction levels, and reduce production costs (including reduction of open ordered slabs, less slabs quality upgrading, reduction of steel-grade changeovers, and reduction of inefficient utilization of tundishes lives). We first formulate the problems as integer-programming models by consider practical constraints and requirements, and then develop the two heuristic algorithms for the corresponding batching problems. By embedding above models and algorithms, we develop decision support system (DSS) software with interactive planning editor. The DSS has been tested by using practical data set collected from the steelmaking plant in Baosteel which is one of the most advanced iron and steel enterprises in China. Computational experiments demonstrate that the models and algorithms developed can generate the satisfactory solutions when they work together with the planning editor in the DSS.     

An asymptotic PTAS for batch scheduling with nonidentical job sizes to minimize makespan

Motivated by the existence of an APTAS (Asymptotic PTAS) for bin packing problem, we consider the batch scheduling problem with nonidentical job sizes to minimize makespan. For the proportional special version, i.e., there exists a fixed number α such that p _j =α s _j for every 1≤j≤n, we first present a lower bound of 3/2 for the approximation ratio and then design an APTAS. Supported by NNSF of China (No.10671108).     

Impacts of buyers' order batching on the supplier's demand correlation and capacity utilization in a branching supply chain

There are several ways for a manufacturer to cope with demand uncertainty, e.g. inventories, capacity and cash. Among these, this study focuses on the second one, the capacity, especially on the problem of investing in flexible facilities and enhancing their utilization via demand management. In a supply chain, demands that an upstream firm (supplier) faces are the purchase orders from the downstream members (buyers). We analyse the impacts of buyers' order batching on the supplier's demand correlation and capacity utilization in a simple branching supply chain, where a supplier does business with two buyers whose market demands are correlated. Our results show that: (i) a supplier whofacesa smaller demand correlation coefficient (i.e. closer to-1) would invest more in flexible facilities; (ii) an increase in order lot size mitigates the correlation of purchase orders; and (iii) a supplier whose facilities are flexible would prefer frequent orders with smaller lots only when market demands are highly negatively correlated. This means that even suppliers whose facilities are flexible would rather prefer infrequent orders with larger lots in the presence of positively correlated demands. Additionally, some managerial implications are discussed.