Managing product variety with mixed make-to-stock/make-to-order production strategy and guaranteed delivery time under stochastic demand

Abstract

Firms often use a facility to produce both Make-to-Stock (MTS) and Make-to-Order (MTO) items. This study provides insights into conditions favoring the adoption of such a mixed MTS-MTO production strategy. Past studies ignore the influence of a one-to-many relation between semi-finished goods and products, and a guaranteed lead-time for MTO products, with uncertain product demand. The problem is modeled as a two-stage stochastic 0–1 integer, non-linear programming problem. In Stage 1, before demand realization, operations determine the product-wise mode of production and inventory level of semi-finished goods/MTS products, and marketing determine the guaranteed lead-time for MTO products. In Stage 2, product demand is realized, and it decreases linearly with lead-time and has a stochastic error component. The demand for MTS products is fulfilled from available inventory, and semi-finished goods are allocated to meet the demand of MTO products and build a stock of MTS products. The objective is to maximize the expected profit per-unit time. Sensitivity analysis of key problem parameters demonstrates that: (1) the integrated-firm can provide smaller lead-times under demand variability, (2) high holding cost of semi-finished goods, high lead-time sensitivity of demand, and high demand variability & low production rate promote mixed strategy over MTO strategy, and (3) high demand variability promotes substitution among semi-finished goods. A Hybrid Greedy and Non-linear Branch & Bound method (featuring problem-specific cuts and search & branching strategy) is proposed to solve real-life problems. This method provides a better solution and a smaller relative gap than commercial solver Simple Branch and Bound.