Optimization models for the tool change scheduling problem

Traditional machine scheduling literature generally assumes that a machine is available at all times. Yet this assumption may not be accurate in real manufacturing systems. In many cases, a machine's tool must be changed after it has continuously worked for a period of time. This paper deals with a single machine scheduling problem subject to tool wear, given the allowed maximum continuous working time of the machine is _TL$T_{\mathrm{L}}$ (tool life) and the tool change time is _TC$T_{\mathrm{C}}$. Job processing and tool changes are scheduled simultaneously. In this paper, we examine this problem to minimize the total tardiness of jobs. Two mixed binary integer programming models are developed to optimally solve this problem. Computational experiments are performed to evaluate the models’ efficiency.     

Critical acceptance values and sample sizes of a variables sampling plan for very low fraction of defectives

Acceptance sampling plans are practical tools for quality control applications, which involve quality contracting on product orders between the vendor and the buyer. Those sampling plans provide the vendor and the buyer rules for lot sentencing while meeting their preset requirements on product quality. In this paper, we introduce a variables sampling plan for unilateral processes based on the one-sided process capability indices _CPU$C_{\mathrm{PU}}$ (or _CPL)$C_{\mathrm{PL}})$, to deal with lot sentencing problem with very low fraction of defectives. The proposed new sampling plan is developed based on the exact sampling distribution rather than approximation. Practitioners can use the proposed sampling plan to determine accurate number of product items to be inspected and the corresponding critical acceptance value, to make reliable decisions. We also tabulate the required sample size n$n$ and the corresponding critical acceptance value _C0$C_0$ for various α$\alpha$-risks, β$\beta$-risks, and the levels of lot or process fraction of defectives that correspond to acceptable and rejecting quality levels.     

A column generation heuristic for dynamic capacitated lot sizing with random demand under a fill rate constraint

This paper deals with the dynamic multi-item capacitated lot-sizing problem under random period demands (SCLSP). Unfilled demands are backordered and a fill rate constraint is in effect. It is assumed that, according to the static-uncertainty strategy of Bookbinder and Tan [1], all decisions concerning the time and the production quantities are made in advance for the entire planning horizon regardless of the realization of the demands. The problem is approximated with the set partitioning model and a heuristic solution procedure that combines column generation and the recently developed _ABCβ${\mathit{ABC}}_{\beta }$ heuristic is proposed.