Bottleneck resource allocation in manufacturing

Many resource-allocation problems in manufacturing and service operations require selecting integer-valued levels for various activities that consume ‘nondecreasing amounts’ of limited resources. System productivity, to be maximized, is limited by the least productive (bottleneck) activity. We first review a basic bisection method that can solve this discrete, monotonic resource-allocation problem even with a nonlinear objective and constraints. We then generalize the basic algorithm to solve an enhanced version of the problem containing additional coupling constraints on the allocation decisions. This generalization applies to assembly-release planning (ARP) in a multiproduct assemble-to-forecast environment with part commonality. The ARP problem requires deciding the number of kits for each product to release for assembly in every time period, using the available parts, to achieve if possible the target service levels for all products and time periods or minimize the maximum deviation of the actual service levels from the targets. We also consider extensions of the ARP model incorporating precedence constraints and part substitutability, and show how to modify the bisection method to solve these problems.