A multifamily dynamic lot-sizing model with coordinated replenishments

Abstract

We consider a multi-item production planning problem where items are grouped together into families. A family setup time is incurred when an item in a family is produced. Also, for each replenishment of a product an individual setup time may be incurred. The objective is to determine the time-phased production schedule that minimizes the total inventory holding cost under demand and capacity constraints. In this article we develop a finite branch-and-bound algorithm for solving the problem. In addition, we present a heuristic procedure to obtain an initial feasible solution. This feasible solution is the initial incumbent solution in the branch-and-bound algorithm and is also used for preprocessing the problem data. Computational results are reported.

A multi-family dynamic lot sizing problem with coordinated replenishments: a heuristic procedure

“…MFDLC can be formulated as an optimization problem. The reader is referred to Erenguc and Mercan (1990) for the optimization model. The heuristic procedure developed in this paper finds the lowest cost production schedule by ignoring the capacity constraint and then adjusts this schedule to achieve capacity feasible production batches.…”

“…For a detailed description of the algorithms developed in these papers the reader is referred to Erenguc (1988). Mercan (1990), and Erenguc and Mercan (1990) proposed the mathematical formulation for MFDLC where the setup structure studied in this paper was introduced through capacity constraints. In addition, these authors developed an exact branch and bound algorithm for solving MFDLC.…”

“…The heuristic procedure for MFDLC was tested on 50 sets of problems whose optimal solutions were provided by Erenguc and Mercan (1990). Each set contained five problems.…”

“…(4) For fixed m and T, percentage difference between the optimal solution and the heuristic solution tends to decrease with r. Erenguc and Mercan (1990) report that obtaining optimal solutions for problem sets A and B require considerably more computing effort than problem sets D and E. The difficulty in solving the problems in sets A and B is attributed to the fact that these problems are 'capacity tight' problems. It is evident from Tables 3-5 and from the discussion above, that the heuristic procedure performed extremely well for the problem sets D and E, and its performance on the harder problems (sets A and B) was very satisfactory.…”

“…Similarly, the time necessary for on-site quality control may be included in the capacity absorption rate. Erenguc and Mercan (1990) developed an exact branch and bound algorithm for solving MFDLC. Their computational experience demonstrated the need for developing effective heuristic procedures for solving MFDLC.…”