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.     

Two-stage time minimizing assignment problem

This paper deals with the optimal selection of m out of n facilities to first perform m   given primary jobs in Stage-I followed by the remaining (n-m)$(n-m)$ facilities performing optimally the (n-m)$(n-m)$ secondary jobs in Stage-II. It is assumed that in both the stages facilities perform in parallel. The aim of the proposed study is to find that set of m   facilities performing the primary jobs in Stage-I for which the sum of the overall completion times of jobs in Stage-I and the corresponding optimal completion time of the secondary jobs in Stage-II by the remaining (n-m)$(n-m)$ facilities is the minimum. The developed solution methodology involves solving the standard time minimizing and cost minimizing assignment problems alternately after forbidding some facility-job pairings and suggests a polynomially bound algorithm. This proposed algorithm has been implemented and tested on a variety of test problems and its performance is found to be quite satisfactory.     

Single cycle policies for the one-warehouse N-retailer inventory/distribution system

We address a multi-echelon inventory system with one-warehouse and N  -retailers. The demand at each retailer is assumed to be known and satisfied by the warehouse. Shortages are not allowed and lead times are negligible. Costs at each facility consist of a fixed charge per order and a holding cost. The goal is to determine single-cycle policies which minimize the average cost per unit time, that is, the sum of the average holding and setup costs per unit time at the retailers and at the warehouse. We propose a O(NlogN)$\mathrm{O}(N\log N)$ heuristic procedure to compute efficient single-cycle policies. This heuristic is compared with other approaches proposed by Schwarz, Graves and Schwarz and Muckstadt and Roundy. We carry out a computational study to test the effectiveness of the heuristic and to compare the performance of the different procedures. From the computational results, it is shown that the new heuristic provides, on average, better single-cycle policies than those given by the Muckstadt and Roundy method.