Joint production and subcontracting planning of unreliable multi-facility multi-product production systems

• Joint subcontracting/production control policy for unreliable multi-facility system.
• Two decision criteria are used simultaneously: cost and customer satisfaction.
• An experimental approach combining statistical methods with simulation is used.
• Significant cost savings were achieved compared to existing model in the literature.
• Subcontracting can replace internal production to achieve a greater service level.

This article addresses the problem of joint optimization of production and subcontracting of unreliable production systems. The production system considered presents a common problem in the pharmaceutical industry. It is composed of multiple production facilities with different capacities, each of which is capable of producing two different classes of medications (brand name and generic). The resort to subcontracting is double: first, it involves the quantity of products received on a regular basis in order to compensate for insufficient production capacity in existing facilities, second, when needed, urgent orders are also launched in order to reduce the risk of shortages caused by breakdowns of manufacturing facilities. Failures, repairs and urgent delivery times may be represented by any probability distributions.The objective is to propose a general control policy for the system under consideration, and to obtain, in the case of two facilities, optimal control parameters that minimize the total incurred cost for a specific level of the customer service provided. Given the complexity of the problem considered, an experimental optimization approach is chosen in order to determine the optimal control parameters. This approach includes experimental design, analysis of variance, response surface methodology and simulation modeling. It allows the accurate representation of the dynamic and stochastic behaviors of the production system and the assessment of optimal control parameters. Other control parameters which represent the subcontracting are introduced and three joint production/subcontracting control policies (general, urgent, regular) are compared to one another. The proposed joint production/regular subcontracting control policy involves a cost decrease of up to 20%, as compared to results obtained by Dror et al. [1], who used a simplified control policy in addition to a heuristic solution approach for a real case study. This policy offers not only cost savings, but is also easier to manage, as compared to that proposed by Dror et al. [1]. Numerical examples and a sensitivity analysis are also performed to illustrate the robustness of the proposed control policy and the solution approach.