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ScienceAsia 27 (2001)

# Calculation of Safety Stock

# PRODUCTION PLANNING METHOD

The safety stocks of finished products must be provided to protect against stock-out problems due to inaccurate demand forecasts. Based on the forecast errors obtained from the demand forecasting models, the amount of the safety stock is calculated using the following formula.^{12 }

SS_{it }=

s f * j * i j

(3)

where SS_{it }= Required safety stock level of product i for period t sf = Safety factor = 1.64 for a required service level of 95 % of the standard normal distribution j = S t a n d a r d d e v i a t i o n o f f o r e c a s t e r r o r s o Group j. _{ij }= Product mix of Product i in Group j. f

Since the errors of the recommended demand forecasting models are lower than those of the current practice, it is clear that SS_{it }based on the use of the models must be lower than that determined from the current practice (assuming that the service levels of both cases are the same). Table 5 presents the required safety stocks of the current practice and the recommended forecasting models at 95 % service level.

The production planning model is developed by initially defining decision variables and parameters, and then mathematically formulating the production planning model. Step 4 of the method requires that the model parameters be estimated and entered into the model. The model is solved for the optimal solution (Step 5). Step 6 recommends that the model parameters are updated, and the model is solved again after one planning period has passed.

The production planning problem of the factory under consideration belongs to the class of multi- stage, multi-item, capacitated production planning model. The models in this class have been discussed extensively in.^{6-11 }They differ in assumptions, ob- jectives, constraints, and solution methods. Our production planning model is a modification of the multi-stage, multi-product model discussed in Johnson and Montgomery.^{6 }Its objective is to minimize the total overtime and inventory holding costs. Costs of laying off and rehiring are not considered because laying off and rehiring are not allowed according to the labor union regulation. Since the production cost is time-invariant and all demands must be satisfied, the regular time production cost is thus not included in the objective function. Relevant parameters and decision variables are defined as follows:

1

1,138

887

2

1,339

1,043

3

1,741

1,356

4

1,540

1,200

5

937

730

6

3,438

2,905

7

1,941

979

8

1,722

868

9

2,324

2,274

10

1,252

1,224

11

7,295

5,258

12

1,463

1,245

13

1,511

1,323

14

507

460

15

1,182

1,072

Table 5. Required safety stock of current practice and of recommended forecasting models.

Parameters :

(rm)_{kt }= Total available regular time excluding preventive maintenance and festival days at stage k for period t (man-hours) (om)_{kt }= Total available overtime excluding preventive maintenance and festival days at stage k for period t (man-hours) = Warehouse capacity (units) = Safety stock of product i for period t (units) = Initial inventory of product i at stage k (units) = Total number of products (15 products) = Total number of periods in the planning horizon (12 periods) = Total number of stages (5 stages) W SS_{it }I_{ik0 }N T K

h_{ik }

= Holding cost per unit of product i at

c_{o }

stage k (baht/unit/period) = Cost per man-hour of overtime labor

d_{it }

(baht/man-hour) = Demand forecast of product i for period

a_{ik }

t (units) = Processing time for one unit of product

Safety stock (units)

i at stage k (hours/unit)

Product

Current Recommended

practi

ce

forecasting models