Problem 2. The following table shows the demand and cost data for a product over the next five weeks Week 12345 Demand40 90 70 40 50 Setup cost 100150200 100 50 Holding cost2312 Determine the timing and size of the orders over the next five weeks using the following heuristics: (a) Silver-Meal (b) Least unit cost The Silver-Meal heuristic method was composed in 19731] by Edward A. Silver and H.C. Meal. It refers to production planning in manufacturing and its purpose is to determine production quantities to meet the requirement of operations at minimum cost. The method is an approximate heuristic for the dynamic lot-size model, perceived as computationally too complex Definition [edit ] The Silver-Meal heuristic is a forward method that requires determining the average cost per period as a function of the number of periods the current order is to span and stopping the computation when this function first increases. Procedure [edit] Define K: the setup cost per lot produced. h: holding cost per unit per period C(T) : the average holding and setup cost per period if the current order spans the next T periods. Let (r1, 2-r3' To satisfy the demand for period 1 rn) be the requirements over the n-period horizon. The average cost- only the setup cost and there is no inventory holding cost. To satisfy the demand for period 1, 2 Producing lot 1 and 2 in one setup give us an average cost: K+hr2 The average cost- (the setup cost+ the inventory holding cost of the lot required in period 2.) divided by 2 periods. To satisfy the demand for period 1, 2, 3 Producing lot 1, 2 and 3 in one setup give us an average cost: Khr22hrs C(3) The average cost =( the setup cost + the inventory holding cost of the lot required in period 2+ the inventory holding cost of the lot required in period 3) divided by 3 periods. In general . C(j) The search for the optimal T continues until C(T) >C(T - 1) Once C)> ), stop and produce ri r2 +-1 And, begin the process again starting from period j. References [edit]