Models of joint economic lot-sizing problem with time-based temporary price discounts

In this research we develop mathematical models of Joint Economic Lot-sizing Problem (JELP) in a situation when a supplier offers time-based temporary price discounts to a buyer during a sale period. To respond this, the buyer places a special order with higher quantity. In literature, it has been assumed that the buyer tends to place the special order at the end of the sale period. We relax this assumption by considering the time when the buyer places the special order during the sale period, i.e., the sooner the special order took place, the higher discount received. In our proposed models called Joint Economic Lot-sizing Problem with Time-based Temporary Price Discounts (JELPTPD) we devide the sale period into k phases. The buyer must place the special order in one of these phases. The highest discount will be given when the special order is placed at the first phase while the lowest one will be given when it is placed at the kth phase. There are two cases discussed. The first case is when the sale period is uniformly divided while the second case is when the sale period is proportionally divided following some rules. Our numerical experiments showed the behavior of the buyer to respond the temporary price discount offers. In major experiments, the buyer shifted the decision on placing the special order in the earlier phases instead of the end of the sale period.