مدیریت سهام های ایمن یکپارچه برای زنجیره تامین چند مرحله ای تحت محدودیت ظرفیت تولید

In the petrochemical, chemical and pharmaceutical industries, supply chains typically consist of multiple stages of production facilities, warehouse/distribution centers, logistical subnetworks and end customers. Supply chain performance in the face of various market and technical uncertainties is usually measured by service level, that is, the expected fraction of demand that the supply chain can satisfy within a predefined allowable delivery time window. Safety stock is introduced into supply chains as an important hedge against uncertainty in order to provide customers with the promised service level. Although a higher safety stock level guarantees a higher service level, it does increase the supply chain operating cost and thus these levels must be suitably optimized. The complexities in safety stock management for multi-stage supply chain with multiple products and production capacity constraints arise from: (1) the nonlinear performance functions that relate the service level, expected inventory with safety stock control variables at each site; (2) the interdependence of the performances of different sites; and (3) finally the margin by which production capacity exceeds the uncertain demand. Given the complexities, the integrated management of safety stocks across the supply chain imposes significant computational challenges. In this research, we propose an approach in which the evaluation of the performance functions and the decision on safety stock related variables are decomposed into two separate computational frameworks. For evaluating the performance functions, off-line computation using a discrete event simulation model is proposed. A linear programming based safety stock management model is developed, in which the safety stock control variables (the target inventory levels used in production planning and scheduling models, base-stock levels for the base-stock policy at the warehouses) and service levels at both plant stage and warehouse stages are used as important decision variables. In the linear programming model, the nonlinear performance functions, interdependence of the performances, and the safety production capacity limits in safety stock management are properly represented. To demonstrate the effectiveness of the proposed safety stock management model, a case study of a realistically scaled polymer supply chain problem is presented. In the case problem, the supply chain is composed of two geographically separated production sites and 3–8 warehouses supplying 10 final products to 30 sales regions.

In the petrochemical, chemical and pharmaceutical industries, supply chains typically consist of multiple stages of production facilities, warehouse/distribution centers, logistical subnetworks and end customers. When events, such as changes in the characteristics of the uncertainties, shifts in the demand to capacity ratio, introduction of a new product and retirement of a matured product, or entrance of new competitors take place, the optimal safety stock level at each stage of the supply chain needs to be re-evaluated. Thus, cost effective and agile safety stock management represents a competitive advantage for a company in a dynamic and highly competitive market. Supply chain performance in the face of various market and technical uncertainties is usually measured by service level, that is, the expected fraction of demand that the supply chain can satisfy within a predefined allowable delivery time window. Safety stock is introduced into supply chains as an important hedge against uncertainty in order to provide the customer with promised service level. Although a higher safety stock level guarantees a higher service level, it does increase the supply chain operating cost and thus these levels must be suitably optimized. The chemical process industry has a history of using deterministic linear programs (LP) and/or mixed integer linear programs (MILP) for production planning and scheduling. In such production planning and scheduling formulations, the notion of safety stock is imbedded by including lower bounds on the inventory levels of various products and/or production sites (Jung, Blau, Pekny, Reklaitis, & Eversdyk, 2004; McDonald & Karimi, 1997). This lower bound is usually referred to as “target inventory level.” The safety stock level is usually defined as the average inventory level measured at a minimum inventory recording time interval. Since the length of periods during which the target inventory constraints are enforced in the planning or scheduling models may be different from the minimum inventory recording time interval, the target inventory level and measured safety stock level usually take different values. Thus, in a production systems using such planning and scheduling models, the target inventory level is the only control variable of the safety stock levels. On the other hand, across diverse sectors of the industry, the base-stock policy (or order-up-to policy) is widely employed for management of pure inventory systems such as warehouses and distribution centers. The base-stock level (or order-up-to level) is the target level of the inventory position that should be constantly maintained. The inventory position is the sum of the amount of orders placed but yet to be delivered and the net inventory level at the site. Thus, the safety stock level for the pure inventory system is controlled by the base-stock levels. Each production or warehouse site in the supply chain exhibits its unique performance functions that relate the service level and the safety stock level to the safety stock control variable of the target inventory or the base-stock level. Evaluating this function for individual products at each site is one of the important issues to be addressed in this research. The estimation of the performance functions for pure inventory systems has attracted a large body of research. Due to their relative simplicity, one can employ simple discrete event simulation-based models for such systems. However, the performance functions of production-inventory systems are dependent on the production planning and scheduling decisions. Therefore, we propose a Sim-Opt based approach to estimate the performance functions of the latter types of production systems. Given the performance functions, it is relatively straightforward to determine the safety stock control variables of individual sites. However, the interdependence of the performance of the upstream supplier and downstream customer site necessitates decision-making with an integrated view of the multi-stage supply chain. Since the performance functions are nonlinear in nature, the integrated management of safety stocks across the supply chain imposes significant computational challenges. In this paper, we discuss the characteristics of and methodology for estimating the nonlinear performance functions, the interdependence between the service levels at different stages and the safety capacity ensuring the sustainability of safety stock level at manufacturing sites along with the methodologies of capturing this system specific characteristic. Finally, we propose a linear programming model that solves the problems of optimal placement of the safety stocks in a multi-stage supply chain. The model incorporates the nonlinear performance functions, the interdependence between the service level at different stages of supply chain and the capacity constraint. To demonstrate the performance of the computational framework, a case study with a realistically scaled polymer supply chain problem is presented. In the case problem, the supply chain is composed of two geographically separated production sites and 3–8 warehouses supplying 10 final products to 30 sales regions.

In this research, we have proposed a linear programming formulation that determines optimal safety stock control variables that minimize the total expected on-hand inventory of the supply chain while ensuring target service level to customers. Discrete event simulation is employed to obtain performance functions at the pure warehouse stages that are operated under a base-stock policy. The Sim-Opt architecture is proposed for modeling the planning and scheduling practice operated in the rolling horizon manner. The convex hull of linear inequalities is used to approximate and model the nonlinear performance functions within the linear programming framework. The accuracy of that approximation is easily and simply controlled by the number of inequalities chosen for representing the convex hull. The computational overhead associated with this construction is very modest as the inequalities are in a single variable. The model addresses the safety capacity that should be provided within the production capacity to maintain certain safety stock level at the production sites. An approximation strategy in the linear programming model is proposed to represent the interdependence between the service levels at the upstream site and downstream site. The linear programming model can be used in determining the safety stock levels for a multi-stage supply chain that has production facilities at the beginning stage of the supply chain. The effects of the lower bounds or target value of service levels at different locations, production frequencies and number of warehouses are investigated with the model. The constructions underlying the linear programming formulation do rely on the normal distribution assumption, which is generally adopted in applications involving stationary demands. Accommodation of non-symmetic distributions, such as the log normal, would require replacing straightforward averaging and inversions conveniently done with the normal distribution with suitable approximations. The extension of this model to the multi-period case that considers anticipatory inventory to cope with non-stationery demands would expand the applicability of this approach to a broader class of situations and is an interesting subject for future research. Incorporation of the “Tight” regime of the safety capacity to the integrated safety stock management model would also be important when a company faces strained production capacity. Future research to develop a model that considers the determination of service times (see work of Graves & Willems, 2000) together with the determination of safety stocks and service levels would also be desirable.