CONWIP Control for Multiproduct Systems

To implement CONWIP control in multiproduct systems, planners must specify not only a total WIP level, but also its allocation to the different products. We describe two methods for setting individual product WIP levels. The first approach focuses on equitably meeting randomly arriving orders for the various products. We designed a heuristic allocation procedure to attain a throughput target. The second approach uses a nonlinear program that bounds the throughput for a given total WIP. The optimal WIP mix is extracted from the upper bounding solution. Both approaches are validated by simulation in numerical examples. Introduction: Research on pull production control policies in general and CONWIP in particular has focused primarily on flow lines that produce one or more similar products. However, the benefits of a limit on work in process (WIP) also can be expected to accrue in multiproduct production systems. Consistent with the increased complexity of producing multiple products, implementing a CONWIP policy is significantly more complicated than in a single product flow shop. First, planners must determine a total WIP level to achieve high total throughput. Second, the total WIP must be allocated to the different products. The proportion of total WIP allocated to each product, the WIP mix, that optimizes system performance generally will not be the same as the product mix. The product mix, specified by the proportions of the total demand on the system that correspond to each product, can be treated as a known parameter vector. But the WIP mix should be influenced by the products’ work contents and the capacities of processing resources. We view it as a vector of decision variables. This paper summarizes two approaches for determining the total WIP and WIP mix. The first approach focuses on equitably meeting randomly arriving orders for the various products. The goal of the second approach is to achieve a high throughput consistent with the product mix. Achieving a Specified Service Level: In a make-to-order system producing multiple product types, the objective is to provide a high customer service level that is equitable across product types, without maintaining excessive WIP. Define the following notation: For product type r R = 1, , : λ r : Arrival rate of orders for type r products. α λ λ r r s s R = = ∑ / 1 : Proportion of all orders over the planning horizon that are for type r. Kr : Number of type r authorization cards in circulation (fixed WIP level for type r). ω λ λ r R R K K ( , , , , , ) 1 1 : Proportion of orders for product type r that are not immediately satisfied. Ω : Specified service level, i.e., the proportion of orders to be satisfied at once. For a given product set with known manufacturing requirements and a given service level the problem of determining the optimal number of authorization cards can be stated as problem (P).