Production planning with resources subject to congestion

Abstract

A fundamental difficulty in developing effective production planning models has been accurately reflecting the nonlinear dependency between workload and lead times. We develop a mathematical programming model for production planning in multiproduct, single stage systems that captures the nonlinear dependency between workload and lead times. We then use outer linearization of this nonlinear model to obtain a linear programming formulation and extend it to multistage systems. Extensive computational experiments validate the approach and compare its results to conventional models that assume workload-independent planning lead times.

Lead time anticipation in Supply Chain Operations Planning

“…For an extensive review of clearing functions, see Pahl et al (2007). Asmundsson et al (2006Asmundsson et al ( , 2009 address the problem of disaggregation for multiitem clearing functions. A single-dimensional clearing function only specifies the relation between an aggregate measure of workload and the aggregate expected output.…”

“…We use the approach proposed by Asmundsson et al (2009) to disaggregate the active processing time in a period. They introduce an allocation variable Z i (t) specifying the proportion of the aggregate output that is of item i and show that the linearization of the clearing function can be formulated as…”

“…This topic is extensively discussed in Asmundsson et al (2009). The specification of the order of processing is undesirable because it restricts the decision space of the PU.…”

Production planning with load-dependent lead times and safety stocks for a single product

“…Kekre (1984) and Ettl et al (2000) follow a similar approach, adding a nonlinear term representing the cost of carrying WIP as a function of workload to the objective function. Graves (1986), Karmarkar (1989), and Asmundsson et al (2006Asmundsson et al ( , 2009 use clearing functions to model the dependency between workload and lead times. Clearing Functions (CFs) express the expected throughput of a resource over a given period of time as a function of some measure of the system workload over that period.…”

“…While this is clearly a very simple environment in which to conduct production planning, our emphasis is on creating an integrated representation of demand uncertainty and workload-dependent lead times, which we believe is challenging in its own right. We incorporate workload-dependent lead times using nonlinear clearing functions (Graves, 1986;Karmarkar, 1989;Asmundsson et al, 2006Asmundsson et al, , 2009. Chance constraints (Charnes and Cooper, 1959) are used to address the uncertain nature of demand.…”