Generalized multi-manufacturer multi-retailer production-delivery supply chain model and its minimum cost solution policy

Production of a product at multiple sources and its deliveries to multiple destinations are a common practice in business. Minimization of the integrated total cost of performing operations and transportation considering the relevant factors such as the minimum order quantity contract, capacities of transport vehicles, and times of transportation in this supply chain is essential, in supplying products to customers at reasonable lesser prices. However, such a supply chain has received little attention in terms of minimizing the integrated total cost taking into account these related factors explicitly. So, there lies a research scope on this topic to fulfill the growing need of minimizing the cost of production-deliveries of products to meet customers’ demands fruitfully. Here we develop such a generalized mathematical model to minimize the integrated total cost of carrying out operations at manufacturers and retailers, and transporting batches (sub-lots) of lots from sources to destinations considering the mentioned realistic constraints. The integrated production-delivery flow is synchronized by delivering lots with batches of equal and/or unequal sizes. First without considering transportation costs, we obtain optimal batches to minimize the total cost of the model. Each of these optimal batches is proportionally distributed at manufacturers as supplies and at retailers as demands. Then the minimum transportation cost solution from manufacturers to retailers is incorporated to the earlier solution to obtain the final result. We illustrate this solution policy with numerical example problems. Sensitivity analyses are performed to see the effect of increasing values of parameters on the minimum total cost.