The classical production-inventory model assumes that both demand and set-up costs are constant. However, in real manufacturing environment, managers usually embark on continuous improvement programmes that often lead to more effective use of tools and machineries and consequently reduction in set-up costs. In fact, constant emphasis on reduction of set-up costs is usually cited as one of the factors responsible for the efficiency of Japanese manufacturing methods. On the other hand, the demand for seasonal product is often characterized by a mixture of time-dependent patterns over the entire season. This paper investigates the effect of learning-based reduction in set-up costs on the optimal schedules and costs of a production-inventory system for deteriorating seasonal products. The demand pattern is a general three-phase ramp-type demand function that represents the various phases of demand commonly observed in many seasonal products in the market. A two-parameter Weibull-distribution function is used for the deterioration of items in order to make the model more generalized and realistic. The study further presents two different multi-period production strategies that can ensure a fast-response to customers’ demand and compare them with the usual single period strategy. The Numerical example and sensitivity analysis shows that learning-based reduction in set-up costs leads to higher production frequency and shorter production runs which are vital aspects of the just-in-time (JIT) philosophy.
This paper presents production-inventory models for deteriorating items with increasing-steady-decreasing demand pattern under the effect of inflation and time value of money. This type of demand behavior can be observed in some fashion products or seasonal products in general. Shortages are allowed with partial backlogging of demand and a two-parameter Weibull-distribution function is used for the deterioration of items in order to make the models more generalized and realistic. The models generate optimal values of initial production run time, onset of shortages, production recommencement time, and total production quantity that minimizes the total relevant costs of production and inventory for any given set of system parameters. Various possible production strategies available for items with variable demand pattern are examined to determine the optimal production strategy. The discounted cash flow approach and trust region optimization methods are used to obtain the optimal results. The Numerical examples and sensitivity analysis show that the optimal production strategy may vary with changes in system parameters.
The primary assumptions with many multi-period inventory lot-sizing models are fixed time horizon and uniform demand variation within each period. In some real inventory situations, however, the time horizon may be unknown, uncertain or imprecise in nature and the demand pattern may vary within a given replenishment period. This paper presents an economic order quantity model for deteriorating items where demand has different pattern with unknown time horizon. The model generates optimal replenishment schedules, order quantity and costs using a general ramp-type demand pattern that allows three-phase variation in demand. Shortages are allowed with full backlogging of demand and all possible replenishment scenarios that can be encountered when shortages and demand pattern variation occur in multi-period inventory modeling are also considered. With the aid of numerical illustrations, the advantages of allowing for variation in demand pattern within replenishment periods, whenever they occur, are explored. The numerical examples show that the length of the replenishment period generated by the model varies with the changes in demand patterns.