In this study, we have studied a joint cyclic production and distribution scheduling problem in a two-stage supply chain with one or more suppliers, one warehouse, and one customer. We have given either optimal approaches or heuristic methods to solve the problem under two policies on production and delivery cycles. For the case with common production and delivery cycle at each supplier (policy (i)), we have proved that there exists an optimal solution where the delivery cycle time from a supplier to the warehouse is an integer multiple of the delivery cycle time from the warehouse to the customer. Based on this property, we have shown that there is a closed-form optimal solution to the problem with a single supplier under policy (i), and developed an efficient heuristic for the general problem under policy (i). The problem under policy (ii), which is more general than policy (i), is solved by a heuristic approach. Both heuristics are shown to perform very well for an extensive set of test problems. We have also computationally evaluated the value of warehouse in our two-stage supply chain. Various managerial insights have been reported.
An important use of this study is to make operational decisions regarding the delivery intervals in a two-stage supply chain. The approaches provided in this paper are easy to implement. Moreover, computationally they are very efficient. The models can also be used to make strategic decisions related to configuring or making changes to a supply chain. For example, we could use the heuristics to choose between a single-stage and a two-stage supply chain. Given that a warehouse has to be built, we could use this study to analyze the total costs corresponding to various locations of the potential warehouse. We could use the heuristics to analyze the trade-offs involved in moving an existing warehouse to a new location. This model can also be used to analyze the effect of reducing the setup cost or setup time on the performance of the entire supply chain. For example, reducing the setup cost or setup time at the supplier would enable more frequent deliveries from the supplier to the warehouse, thus saving on the average inventory costs. A trade-off between this savings and the increase in the total transportation costs and the expenses related to reducing the setup time and costs can be used to analyze whether it is worth trying for a reduction in the setup cost or time.