Silver-Meal heuristic
Encyclopedia
The Silver-Meal heuristic method was composed in 1975 by E.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.
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.
K: the setup cost per each 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, r2, r3, …….,rn) be the requirements over the n-period horizon.
To satisfy the demand for period 1
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:
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:
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,
The search for the optimal T continues until C(T) > C(T‐1).
Once C(j) > C(j-1), stop and produce r1+ r2+ r3+ ... +rj-1
And, begin the process again starting from period j.
Definition
Silver-Meal heuristic is a forward method that requires determining the average costAverage cost
In economics, average cost or unit cost is equal to total cost divided by the number of goods produced . It is also equal to the sum of average variable costs plus average fixed costs...
per period as a function of the number of periods the current order is to span and stopping the computation
Computation
Computation is defined as any type of calculation. Also defined as use of computer technology in Information processing.Computation is a process following a well-defined model understood and expressed in an algorithm, protocol, network topology, etc...
when this function first increases.
Procedure
Define :K: the setup cost per each lot produced.
h: holding cost
Holding cost
In business management, holding cost is money spent to keep and maintain a stock of goods in storage.The most obvious holding costs include rent for the required space; equipment, materials, and labor to operate the space; insurance; security; interest on money invested in the inventory and space,...
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, r2, r3, …….,rn) be the requirements over the n-period horizon.
To satisfy the demand for period 1
- C(1)= K
The average cost = only the setup cost and there is no inventory
Inventory
Inventory means a list compiled for some formal purpose, such as the details of an estate going to probate, or the contents of a house let furnished. This remains the prime meaning in British English...
holding cost.
To satisfy the demand for period 1, 2
Producing lot 1 and 2 in one setup give us an average cost:
- C(2) = (K+(h*r2))/2
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:
- C(3) = (K+(h*r2)+(2hr3))/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) = (K+hr2+2hr3+. . . . . +(j-1)hrj) / j
The search for the optimal T continues until C(T) > C(T‐1).
Once C(j) > C(j-1), stop and produce r1+ r2+ r3+ ... +rj-1
And, begin the process again starting from period j.