The Silver–Meal heuristic is a
production planning
Production planning is the planning of Production (economics), production and manufacturing modules in a company or industry. It utilizes the resource allocation of activities of employees, raw material, materials and production capacity, in orde ...
method in manufacturing, composed in 1973
[EA Silver, HC Meal, A heuristic for selecting lot size quantities for the case of a deterministic time-varying demand rate and discrete opportunities for replenishment, Production and inventory management, 1973] by Edward A. Silver and H.C. Meal. 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
The Silver–Meal heuristic is a forward method that requires determining the
average cost In economics, average cost or unit cost is equal to total cost (TC) divided by the number of units of a good produced (the output Q):
AC=\frac.
Average cost has strong implication to how firms will choose to price their commodities. Firms’ sale ...
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
Define :
''K'': the setup cost per lot produced.
''h'':
holding cost
In marketing, carrying cost, carrying cost of inventory or holding cost refers to the total cost of holding inventory. This includes warehousing costs such as rent, utilities and salaries, financial costs such as opportunity cost, and inventory co ...
per unit per period.
''C(T)'' : the average holding and setup cost per period if the current order spans the next T periods.
Let (r
1, r
2, r
3, …….,r
n) 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 r
1 + r
2 + r
3 + ... + r
j − 1
And, begin the process again starting from period j.
See also
* Infinite fill rate for the part being produced:
Economic order quantity
Economic Order Quantity (EOQ), also known as Economic Buying Quantity (EPQ), is the order quantity that minimizes the total holding costs and ordering costs in inventory management. It is one of the oldest classical production scheduling models. ...
* Constant fill rate for the part being produced:
Economic production quantity
The economic production quantity model (also known as the EPQ model) determines the quantity a company or retailer should order to minimize the total inventory costs by balancing the inventory holding cost and average fixed ordering cost. The EPQ m ...
* Demand is random: classical
Newsvendor model The newsvendor (or newsboy or single-periodWilliam J. Stevenson, Operations Management. 10th edition, 2009; page 581 or salvageable) model is a mathematical model in operations management and applied economics used to determine optimal inventory l ...
* Demand varies over time:
Dynamic lot size model
The dynamic lot-size model in inventory theory, is a generalization of the economic order quantity model that takes into account that demand for the product varies over time. The model was introduced by Harvey M. Wagner and Thomson M. Whitin in ...
References
*Production and Operations Analysis by S. Nahmias, McGraw-Hill
{{DEFAULTSORT:Silver-Meal heuristic
Mathematical optimization in business