Chia-Kuan Ting

Replenishment run time problem with machine breakdown and failure in rework

This paper studies the optimal replenishment run time for a production system with stochastic machine breakdown and failure in rework. In most real world manufacturing processes, generation of defective items and random breakdown of equipment are inevitable. This research addresses such reliability issues by examining a production system with a Poisson breakdown rate and an imperfect reworking process. When machine breaks down, no-resumption policy is adopted. Under such a policy, the present production run is aborted and will be restarted only when all on-hand inventories are depleted. Mathematical modeling is used. Derivations of production- inventory cost functions and proofs of theorems and proposition are presented, with the objective of determination of the optimal replenishment run time and lot size that minimize the expected costs per unit time. An illustrating example is provided to show its practical usage.

Production-delivery policy with imperfect rework and a revised shipping plan derived without derivative

Abstract This paper uses algebraic techniques to derive a production-delivery policy with imperfect rework and a revised shipping plan. A production system with the reworking of defective items produced is considered. A portion of reworked items fails during the repairing. A revised (n + 1) shipping plan aiming at reducing inventory holding costs is adopted for delivering finished items to buyers. Without using differential calculus, this paper demonstrates that the optimal policy can be derived. It will be helpful to practitioners who may not have sufficient knowledge of calculus to understand with ease such a realistic inventory system.

Solving production lot size problem with an improved delivery policy and failure in rework by a simplifi ed solution procedure

A simplifi ed solution procedure is proposed in this paper to solve a specifi c production lot size problem with an improved delivery policy and failure in rework. Unlike the conventional method using differential calculus with the need for proving optimality of the longrun average cost function, this paper demonstrates that the optimal lot size and its related costs for the aforementioned production model can be derived without derivatives. Such an approach may enable practitioners who with little knowledge of calculus to understand with ease the realistic production-shipment integrated systems

Solving fi nite production rate model with scrap and multiple deliveries

This paper examines fi nite production rate (FPR) model with scrap and multiple deliveries. Classic FPR model assumes continuous issuing policy for satisfying demand and perfect quality production for all items produced. However, in real life vendor-buyer integrated system, multiple shipment policy is practically used and generation of defective items during a production run is inevitable. Mathematical modeling and analysis is used, renewal reward theorem is employed to cope with the variable production cycle length, and the integrated long-run average cost per unit time is derived. A closed-form optimal batch size solution to the problem is obtained. A numerical example demonstrates its practical usage