A comparison between two pricing and lot-sizing models with partial backlogging and deteriorated items

Recently, Abad [2003. Optimal pricing and lot-sizing under conditions of perishability, finite production and partial backordering and lost sale, European Journal of Operational Research, 144, 677-685] studied the pricing and lot-sizing problem for a perishable good under finite production, exponential decay, partial backordering and lost sale. In this article, we extend his model by adding not only the backlogging cost but also the cost of lost goodwill. We then analytically compare the net profits per unit time between Abad's (2003) model and Goyal and Giri's [2003. The production-inventory problem of a product with time varying demand, production and deterioration rates. European Journal of Operational Research, 147, 549-557] model. In Abad's model, the cycle starts with an instant production to accumulate stocks, then stops production to use up stocks, and finally restarts production to meet the unsatisfied demands. By contrast, in Goyal and Giri's model, the cycle begins with a period of shortages, then starts production until accumulated inventory reaches certain level, and finally stops production and uses up inventory. Our theoretical results show that there is no dominant one between these two models. Furthermore, we provide certain conditions under which one model has more net profit per unit time than the other. Finally, we give several numerical examples to illustrate the results.