Two Product, Two Region Production, Inventory, and Transportation Problems

Abstract

A deterministic production and transportation planning problem is considered over a finite time horizon for two products that can be produced in each of two regions. Each region uses its own facility to supply the demands for two products. Demands for product 2 in one region can be satisfied either by its own production or by transportation from other region, while no transportation between two regions is allowed for product 1. Production, inventory and transportation costs are assumed to be non-decreasing and concave. The objective is to find the schedule of production and transportation in each region by which the total cost over the horizon is minimized. Using a network flow approach, we develop a dynamic programming algorithm that can find an optimal policy.

Modeling the Two-Region, Two-Product Capacitated Production and Transportation Problem

“…In this paper, we extended the approach developed in the previous paper [1] to time-dependent capacity bounds on transportation. Using a network flow approach, properties of extreme points were identified.…”

“…In the problem, we assume that the transportation is allowed only for product 2 from one region to another. A deterministic production and transportation planning problem for two products that can be produced in each of two regions and transported between two regions was examined in [1]. We extend the approach developed in the previous paper [1] to time-dependent capacity bounds on transportation.…”

“…Such a model that multi-products are produced by a facility in each region and some of them can be transported from the other region to meet the demand occurs frequently in manufacturing industries such as chemical industry and machinery (or food) industry. [1] The problem addressed in this paper is meaningful in that the transportation capacity is additionally considered to impart a sense of reality as an extension of the previous model.…”