Process Mean Determination with Quantity Discounts in Raw Material Cost*

Abstract

Setting the mean (target value) for a container-filling process is an important decision for a producer when the material cost is a significant portion of the production cost. Because the process mean determines the process conforming rate, it affects other production decisions, including, in particular, the production setup and raw material procurement policies. In this paper, we consider the situation in which quantity discounts exist in the raw material acquisition cost, and incorporate the quantity-discount issue into an existing model that was developed for simultaneously determining the process mean, production setup, and raw material procurement policies for a container-filling process. The product of interest is assumed to have a lower specification limit, and the items that do not conform to the specification limit are scrapped with no salvage value. The production cost of an item is proportional to the amount of the raw material used in producing the item. A two-echelon model is formulated for a single-product production process, and an algorithm is developed for finding the optimal solution. A sensitivity analysis is performed to study the effects of the model parameters on the optimal solution. Subject Areas: Probability Models, Production and Inventory Control, and Purchasing.

Economic selection of process mean and lot‐sizing decisions for multi‐newsvendor supply chain

“…Moreover, the producer's average inventory cost in a selling period is . As in Al‐Fawzan and Hariga (), Roan et al (), and Gong et al (), we assume that the direct production cost is a linear function of number of items produced and is given by βQ , where β is the cost of producing one item, consequently, the producer total cost per selling period ( TC P ) is …”

“…Recently, many models that integrate the targeting problem with lot‐sizing decisions in production environment have been developed by many researchers. For example, Gong et al () addressed the economical selection of process mean and lot‐sizing decisions for a production process where the process mean is constant during the production run and the producer is subjected to deterministic demand. This model is extended by Roan et al () by considering production lot size, raw material procurement policy, and the targeting problem in one model.…”

An integrated inventory-targeting problem with time-dependent process mean

“…It should be noticed that this cost term was not included in the material purchasing cost of Gong et al (1998) even though it a ¶ ects the selection of the setting of the initial process mean. Consequently, the total material ordering, acquisition, and inventory holding cost per unit of time is…”

“…Consider the example problem solved in Gong et al (1998) This form has been considered by Gong et al (1998). The solution is · * 0ˆ1 :557 and t * pˆ2 :425, with a total cost of $6551.49.…”

“…Traditionally, inventory and production issues were not addressed in the targeting problem. The work of Roan et al (1995) and Gong et al (1998) both t in the rst category (i.e., the STP). The objective of their model is to nd the optimum process mean, order quantity, and production lot size.…”