Abstract
In recent decades, the integrated manufacturer-buyer supply chain problem has been widely studied by many scholars, as it provides benefits to both parties in terms of planning flexibility, information sharing and joint costs. The manufacturer produces a production lot of size Q, with variable production rate P ≤ U, where U denotes the maximal production rate (e.g., due to technological restrictions or due to limited machinery and/or manpower capacities). The manufacturer delivers the lot to the buyer in n (integer) smaller shipments, each of size q. An upper bound on the production cycle length is assumed (e.g., to enable the scheduling of maintenance periods or idle windows of time in which workers are not required to work.) In order to solve the problem mathematically, we suggest a sub-optimal nested formulation of the problem that utilizes existing formulas for n*(r) and q*(r) (where r denotes the demand-to-production rate ratio, r = D/P) for the unconstrained problem. The optimal solution of the accurate formulation is obtained through numerical optimization, utilizing the IBM CPLEX solver, and is compared with the proposed sub-optimal method. Among the advantages of the suggested approach are that the solution is analytically derived, it is very simple to implement, and it yields a minimal joint cost that is close to the accurate formulation.
Highlights
The joint optimization concept for buyer and vendor was first described by Goyal [1]
An unlimited cycle length reduces planning flexibility, whereas a bound on the production cycle allows utilization of the time when the production system is idle for processing other products
The following assumptions are used in our model: (1) all parameters are fixed and known (2) the unit cost to the manufacturer is independent of the production rate (3) both players share information and have an agreement regarding sharing the joint profit (4) the production rate is bounded from above (5) the production rate is greater than the demand rate (6) the production cycle length is bounded (7) shipment frequency is an integer (8) each production lot incurs a production set-up cost (9) each shipment incurs a delivery cost
Summary
The joint optimization concept for buyer and vendor was first described by Goyal [1]. There is evidence to suggest that improved synchronization of the production and purchasing processes between the manufacturer and the buyer, as well as greater information sharing, are the most effective means of meeting demand and increasing profits along the supply chain. An unlimited cycle length reduces planning flexibility, whereas a bound on the production cycle allows utilization of the time when the production system is idle (i.e., the delay between production lots) for processing other products. Such delays allow workers free time (e.g., for personal or career-development purposes). The engineers set the equipment to make 1989 models after the workers had left the factory on Friday afternoon, ran the equipment to manufacture the new models over the weekend, and reset the equipment to produce 1988 model cars so that regular production could be resumed on Monday morning
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