Computer simulation of lot‐sizing algorithms in three‐stage multi‐echelon inventory systems

Abstract

Abstract This paper evaluates conventional lot‐sizing rules in a multi‐echelon coalescence MRP system. A part explosion diagram of three levels and twenty‐one nodes is simulated using FORTRAN IV Level G. Nine separate lot‐sizing methods were evaluated in this analysis. These methods included Lot for Lot, Economic Order Quantity, Periodic Order Quantity, Least Total Cost, Least Unit Cost, Part‐Period Balancing, the Silver‐Meal Algorithm, and the Wagner‐Whitin Algorithm. A hybrid rule using both the Economic Order and the Economic Production Quantity rules was also evaluated. The performance of each lot sizing rule was simulated over nine different sets of market requirements patterns over a twelve month period. The types of demand variation included a constant rate, three different patterns of normally distributed demand, a random pattern, and two cyclic patterns. A hybrid pattern was used which equally weighted components of constant, random, normal, and cyclic demand. Finally, the ninth pattern consisted of actual data obtained from a job shop manufacturing facility. Within the part explosion diagram, ratios of setup cost to carrying cost, “goes into” quantities, and lead times were assigned for each node. Assigned values were selected from uniform distributions with prespecified ranges. A computer model was developed to perform the simulation. It consisted of an executive program, a routine for data generation, and separate routines to exercise each of the different lot‐sizing rules. The simulations were conducted under three operational rules. The first rule allowed for the establishment of initial inventories just large enough to “cover” those gross requirements that occurred prior to the time the first order arrived. Carrying costs for this stock were included in the computation of total costs per node. The second rule provided for the delay of application of each lot sizing rule. This avoided receiving an order in a period of zero demand. The third rule addressed the computation of costs. The total cost was computed on the basis of average inventory level and the number of required setups. The analysis required the completion of 1701 separate simulation runs (9 rules X 9 demand patterns X 21 nodes). The performance of each rule was evaluated on the basis of total annual inventory cost. The Periodic Order Quantity (POQ) rule performed best in six of the nine demand patterns analyzed. In two of the remaining three cases, it ranked second on the basis of minimizing costs. The Least Unit Cost (LUC), Least Total Cost (LTC), and Pan‐Period Balancing (PPB) algorithms demonstrated identical performance in four of the demand patterns analyzed. Generally, they ranked in the upper half of the rules evaluated. The Economic Order Quantity (EOQ) and the Economic Order/Production Quantity hybrid rules performed only moderately well. On the basis of cost, the consistent worst performers were the Wagner‐Whitin (WW), Silver‐Meal (SM), and Lot‐for‐Lot (LFL) rules. It was found that gross requirements tend to occur sporadically in different levels of the system. Order policies of parent nodes often cause the policies in higher level nodes to resemble the lot‐for‐lot order philosophy, regardless of the rule being used. Because of this phenomenon, those rules that generate fewer orders over the planning horizon for parent nodes often tend to perform better on the basis of total inventory cost.

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