A mathematical model for optimal discount setting of capacity-constrained service centers with shortage cost and demand shifting - Boydon, Christian John Immanuel S.
A common problem in service centers is the imbalance of capacity and demand translating to underutilized time periods even though there are time periods experiencing shortage. This leads to shortage cost and missed opportunities so there is a rationale to optimize profit. In this paper specifically, promotional discounts are utilized and a mathematical model to maximize profit is created for service centers with fixed capacity and time-varying demand which leads to shortage and underutilization. Given demand shifts between time periods due to the discount, the decision to be solved is when and how much to offer promotional discounts such that profit is maximized while balancing these three factors: a) decrease in shortage cost when demand shifts shortage time periods, b) increase in revenue (realize missed opportunities) when demand shifts to underutilized time periods, and c) decrease in revenue due to lower prices when discount is applied. The mathematical model uses a simple function for shifting demand and is easy to solve, i.e. optimal solution is guaranteed in fast solving time. A methodology was created so that mathematical model can be used by any service center manager. This methodology includes cutting time interval under study into discretized time periods, determining average demand per time period, establishing a demand shifting function, and running a program to determine optimal discount per time period. The demand shifting function was based on a previous paper on demand service centers but with a different factor used for practical reasons. The mathematical model was analyzed and validated through a theoretical proof showing that it is a convex set in its entire search space thus is easy to solve. Illustrations were done and the methodology was applied to a particular service center followed by sensitivity analysis to get insights on the arbitrary parameters. Ultimately, it was shown that the model can give the optimal discount setting to maximize profit of a service center with the specifications as detailed above in fast solving speed and if the parameters are known.