Dynamic lot size problems with one-way product substitution

Abstract

We consider two multi-product dynamic lot size models with one-way substitution, where the products can be indexed such that a lower-index product may be used to substitute the demand of a higher-index product. In the first model, the product used to meet the demand of another product must be physically transformed into the latter and incur a conversion cost. In the second model, a product can be directly used to satisfy the demand of another product without requiring any physical conversion. Both problems are computationally intractable in general. We develop dynamic programming algorithms that solve the problems in polynomial time when the number of products is fixed. A heuristic is also developed, and computational experiments are conducted to test the effectiveness of the heuristic and the efficiency of the optimal algorithm.

Forecast and rolling horizons under demand substitution and production changeovers: analysis and insights

“…The notion of substitution has recently been recognized as an effective tool to improve the efficiency of multi-product inventory systems by taking advantage of the inherent flexibility. Substitution usually takes two forms, namely, consumer driven (Ansari et al, 1994(Ansari et al, , 1998Van Ryzin and Mahajan, 1999;Rajaram, 2001;Rajaram and Tang, 2001;Honhon et al, 2010) or manufacturer driven (Robinson, 1990;Drezner et al, 1995;Gurnani and Drezner, 2000;Rudi et al, 2001;Axsater, 2003;Hsu et al, 2005). Under the former strategy, consumers choose an alternate product when their original choice is unavailable.…”

“…None of these studies, however, consider the possibility of substitution between products. Hsu et al (2005) study a multi-product DLS model with one-way substitution: a product with a lower index can substitute demand for a product with a higher index. They show that their models are NP-hard and use dynamic programming to develop effective algorithms for practically relevant instances.…”

Optimal policy for a muti-product, multi-period, non-stationary, stochastic production and customization problem

“…The first one is that our model differs from the models in the literature. The key differences between our model and the multi-product substitution models in the literature are that the multi-product substitution models in the literature focus on either single-period problems (Deuermeyer, 1980;Bassok et al, 1999;Hsu and Bassok, 1999;Rao et al, 2004) or multi-period problems with deterministic demands (Hsu et al, 2005), while our model is a multi-period and non-stationary model with stochastic demands. The key differences between our model and the multi-product delayed product differentiation problems in the literature are in the following three ways: (1) unlike the models studied by Eppen and Schrage (1981), Federgruen and Zipkin (1984a, 1984b, 1984c, and Aviv and Federgruen (2001), which do not allow the firm to hold the inventory of the generic product, our model allows the firm to do so.…”

“…Rao et al (2004) study a singleperiod, multi-product problem with downward substitution and setup cost for production and study heuristics. Hsu et al (2005) study multi-period, multi-product, dynamic lot size problems with full downward substitution. They assume that demands in each period are deterministic and study the optimal and heuristic solutions.…”

Retail inventory management with stock-out based dynamic demand substitution

“…The primary objective is to minimize the sum of production, inventory holding, and, in some cases, product conversions costs. A detailed discussion of the relevant literature on supplier-controlled substitution is presented in Hsu et al (2005) and Rao et al (2004).…”