An inventory replenishment policy for deteriorating items with shortages and partial backlogging

It has long been assumed that the shortages in inventory systems are either completely backlogged or totally lost. However, it is more reasonable to characterize that the longer the waiting time for the next replenishment, the smaller the backlogging rate would be. Moreover, the opportunity cost due to lost sales should be considered since some customers would not like to wait for backlogging during the shortage periods. Without considering these two realistic conditions, study on the inventory modeling for deteriorating items with shortages and partial backlogging cannot be complete and general. In the present article we define an appropriate time-dependent partial backlogging rate and introduce the opportunity cost due to lost sales. Numerical examples are also presented to illustrate the effects of changes in backlogging parameter and unit opportunity cost on total cost and the optimal number of replenishments.Scope and purposeIn a recent article published in this Journal, Giri et al. (Comput. Oper. Res. 27 (2000) 495–505) implemented an existing procedure to the inventory problem of Hariga and Al-Alyan (Comput. Oper. Res. 24 (1997) 1075–83) which concerns with lot-sizing heuristic for deteriorating items with shortages allowed in all cycles except the last one. Giri et al. deviated from the traditional practice and suggested a new policy allowing shortages in all cycles over a finite planning horizon. Their numerical results indicated the proposed policy is cheaper to operate with a cost reduction up to 15%. However, they did not consider the opportunity cost due to lost sales that happen because customers would not like to wait for backlogging. Moreover, for many products with growing sales, the length of the waiting time for the next replenishment is the main factor for determining whether the backlogging will be accepted or not, and the backlogging rate is expected to be time-dependent. Thus the assumption made in Giri et al. that the backlogging rate is a fixed fraction of the total amount of shortages is not reasonable.The purpose of this paper is to present a more realistic discussion of the inventory problem for deteriorating items with time-varying demands and shortages over a finite planning horizon. In contrast to the model by Giri et al., we define an appropriate partial backlogging rate and introduce the opportunity cost due to lost sales. We attempt to complement their model as a practical and general solution for inventory replenishment problems. With these extensions, the scope of applications of the present results is expanded.     

A note on ‘A two-level supply chain with consignment stock agreement and stock-dependent demand’

This note points out that the cost functions within Zanoni and Jaber [Zanoni, S. and M. Y. Jaber. 2015. “A Two-level Supply Chain with Consignment Stock Agreement and Stock-dependent Demand.” International Journal of Production Research 53: 3561–3572] might be incorrect due to misuse of demand representation. By incorporating Braglia and Zavanella’s consignment stock model and relaxing the zero-inventory reordering constraint, Zanoni and Jaber made extensions of the integrated vendor–buyer supply chain with stock-dependent demand in Sajadieh, Thorstenson, and Akbari Jokar’s proposed model. However, Sajadieh, Thorstenson, and Akbari Jokar’s model has different scenarios than Braglia and Zavanella’s model, and these inconsistencies cause false formulation in Zanoni and Jaber’s paper. In this note, we first formulate the justified cost functions and then present characteristics of the corrected model.     

A Case Study for Reducing Client Waiting Time in a Health Evaluation Center Using Design for Six Sigma

Abstract:

Long waiting times in health evaluations are an unnecessary waste of resources. This case study focuses on the Health Evaluation Center in the Chang Gung Medical Center in Taiwan and demonstrates an empirical application of reducing waiting time by using the Design for Six Sigma method. We redesigned the health evaluation process and proposed a method to develop a new capable system with radio frequency identification (RFID) technology. Client waiting time and total cycle time of the process were reduced by 56% and 40%, respectively.