Material Requirements Planning Systems

INTRODUCTION

The lot sizing problems with time varying demands have been widely studied because of their key role in Material Requirements Planning systems. Majority of researches were on deterministic demand condition. Unfortunately, due to forecast errors, assuming demand as deterministic did not give positive results most of the time. Therefore, new approach was necessary, and the result was stochastic lot sizing. The advocates of stochastic lot sizing claim that, it is much more close to reality than deterministic case. There has been extensive research on this area in recent years. One of the prominent works on stochastic lot sizing was done by Bookbinder and Tan. The "static dynamic uncertainty" strategy of Bookbinder and Tan (Tarim and Kingsman, 2004) is a heuristic in which two-stage process of firstly fixing the replenishment periods and then secondly determining what adjustments should be made to the planned orders as demand is realized. The total cost, composed of ordering and inventory holding costs, is minimized under a minimal service level constraint.

Tarim and Kingsman (Tarim and Kingsman, 2004) in the current paper reformulate and solve the Bookbinder and Tan heuristic. They claim that, even though Bookbinder and Tan heuristic was one of the best attempts to get an optimal solution in stochastic lot sizing case, it was not optimal and had some disadvantages. Thus, they projected a mixed integer programming formulation to solve the stochastic dynamic lot sizing problem by optimally under the static dynamic uncertainty strategy of Bookbinder and Tan.

In this paper, they consider meeting a specified customer service case where they use "minimum service level" criterion. Demand is not deterministic with different values in each period. The service level criterion is defined as specifying a minimum probability (α). So that the net inventory at the end of each period will not be negative.

PROBLEM STATEMENT

There are two ways to formulate the stochastic dynamic lot sizing problem. First way is, by assuming that for every stock out there is a penalty cost and the second way is by minimizing setup and inventory cost or expected total cost subject to satisfying some customer service level criterion.

In the current paper, the second method is chosen, that is the problem is solved by minimizing the expected total cost over the N period planning horizon subject to the service level constraints as given below:

As mentioned above, the expected total cost consists of setup cost, inventory holding cost and replenishment order cost, and therefore we minimize the sum of these costs subject to the service-level constraints.

The service-level constraints are as follows:

δ_(t )= {█(1,&If X_t>0@0,& otherwise )┤ t=1,…..,N