A Case Study

In Section 18.4 attention has been paid to the mathematical modeling of an inte­grated LP problem using MINLF. Based on this formulation, this section presents a medium-sized case study and uses GAs to find the optimal logistics plan for a company producing and distributing home gym equipments. The following subsec­tions will discuss the case problem, the optimization procedure, and the results achieved.

Case Problem

Body shape group (BSG) has four manufacturing plants, four warehouses, and five customer zones (end users) in major cities in Australia. BSG manufactures and dis­tributes six types of home gyms (/'i — /₆), including two types of benches (/| and Ь), two types of stack machines (i₃ and /₄), and two types of plate-loaded machines (/5 and i₆). Plants 1 and 2 (m.\ and m₂) are located in Sydney and Melbourne and are able to produce all six types of products. Plant 3 (w₃) in Adelaide can only pro­duce benches and stack machines (i'| — i₄), and m₄ in Perth is able to produce stack machines and plate-loaded machines (z'₃ — /₆). The planning horizon for the pro­posed LP problem is 1 year, which comprises 12 equal periods of 1 month (/| — '12)- The aggregated demands for the six types of products at four end users are known at every period of the planning horizon. Also known are the BSG manufacturing and distribution data, including production and outsourcing costs for each product type, inventory holding costs, transportation costs, and backlogging costs.

Production capacity constraints as well as holding and distribution capacity at stack buffers and warehouses are known for this case study. BSG has cer­tain production and storage capacity constraints at each manufacturing plant, backlogging limitations enforced from the customers, and holding and distribu- tion capacity constraints at its stack buffers and warehouses. Partial delivery is ⁿ°t allowed in this case problem, which implies that the customer demand for each product at each end user is to be delivered in one lot; otherwise, the associated demand will be backordered in order to be satisfied in subsequent Periods.