The main purpose of this study is to investigate the periodic inventory model with backorder price discounts, where shortages are partially backlogged. The application of just-in-time (JIT) philosophy i.e., crashing of the lead-time and setup cost has been carried component wise. Two cases have been discussed viz 1 protection interval demand distribution is known (normal distribution approach) ...

This paper examines an economic production quantity (EPQ) model with rework and service level constraint. First, we prove that the expected overall costs for an imperfect EPQ model with backlogging permitted is less than or equal to that of the one without backlogging. Secondly, the relationship between “imputed backorder cost” and maximal shortage level is derived for decision-making on whethe...

This paper considers a dynamic lot size problem faced by a producer who supplies a single product to multiple customers. Characterized by their backorder costs as well as shipping costs, the customer with a high backorder cost is the one whose need for the product is more critical than the need of a customer with a low backorder cost. We show that the general problem with time-varying, customer...

This paper deals with a multi-period fixed charge production-distribution problem associated with backorder and inventories. The objective is to determine the size of the shipments from each supplier and backorder and inventories at each period, so that the total cost incurred during the entire period towards production, transportation, backorder and inventories is minimised. A 0-1 mixed intege...

In this paper, we consider the pricing and lot-sizing problem for a product subject to general rate of deterioration and partial backordering. We use impatience functions to model backlogging of demand. We show that even when lost sale and backorder costs are present, the problem is well posed in the reduced space. We provide an iterative procedure for solving the overall problem. We describe s...

In this paper, we consider fuzzy inventory with backorder. First, we fuzzify the storing cost a, backorder cost b, cost of placing an order c, total demand r, order quantity q, and shortage quantity s as the triangular fuzzy numbers in the total cost. From these, we can obtain the fuzzy total cost. Using the signed distance method to defuzzify, we get the estimate of the total cost in the fuzzy...

The inventory models analyzed in this paper explore the problem in which the lead time and ordering cost reductions are inter-dependent in the continuous review inventory model with backorder price discount. The objective is to minimize total related cost by simultaneously optimizing the order quantity, reorder point, lead time and backorder price discount. Moreover, we assume that the mean and...

A kit is a specific collection of components and/or tools needed for completing a procedure or producing a product. A multiperiod material planning system for production kits under the demand and procurement lead-time uncertainty is considered when component sharing among kits is plausible. Simulation experiments show that component sharing improves the system’s service measure of average kit a...

We consider a single-item make-to-stock production system. The item is demanded by several classes of customers with different backorder costs. The item can also satisfy demands from a salvage market without a backorder cost. Item processing times have an Erlang distribution. This allows us to model the information on the production status in a tractable way. We fully characterize the optimal s...

Abstract This paper considers the economic production quantity (EPQ) problem with backorder in which the setup cost, the holding cost and the backorder cost are characterized as fuzzy variables, respectively. Following expected value criterion and chance constrained criterion, a fuzzy expected value model (EVM) and a chance constrained programming (CCP) model are constructed. Then fuzzy simulat...