Abstract
Supply chain is an accepted way of remaining in the competition in today's rapidly changing market. This paper presents a coordinated seller-buyer supply chain model in two stages, which is called Joint Economic Lot Sizing (JELS) in literature. The delivery activities in the supply chain consist of a single raw material. We assume that the delivery lead time is stochastic and follows an exponential distribution. Also, the shortage during the lead time is permitted and completely back-ordered for the buyer. With these assumptions, the annual cost function of JELS is minimized. At the end, a numerical example is presented to show that the integrated approach considerably improves the costs in comparison with the independent decisions by seller and buyer.
Highlights
Chain takes on an importance because of the rapid market changes which is the result of the explosion of product varieties with short life cycles in today’s global market (Ben-Daya et al 2008)
One major subject in this topic is managing the inventory across the whole supply chain to reduce the costs for customers (Soroor et al 2009a)
As mentioned by Goyal (1977) and Ouyang et al (2004), the total benefit under integrated optimization should be shared by both parties to encourage them to cooperate together
Summary
Chain takes on an importance because of the rapid market changes which is the result of the explosion of product varieties with short life cycles in today’s global market (Ben-Daya et al 2008). Definition of the problem Model notation The model is a supply chain which represented a seller with a constant produce rate of ‘p’, and his product is sent to a buyer by shipment equal size of ‘Q’. Model formulation To obtain the buyer’s expected total cost per unit time, TCb(r,Q), it is considered that the orders are received in a sequence which are not necessarily the same as they have been made. Considering the demand rate as D, from the time of ordering in which the inventory position is r until the time r/D current cycle inventory vanishes and after this time if a new lot reaches, shortage cost should be paid because the shipment size is Q. Solution for separate and joint models First, we consider solution for the case in which the seller and buyer optimize their total cost functions separately. It is not necessary to focus on the method of finding optimal solution of JTC (when n is fixed), TCb and TCv because general methods like derivative-free method in many types of software such as MATLAB (MathWorks, Natick, MA, USA) can solve this problem
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