Question

Jerusalem Medical Ltd., an Israeli producer of portable kidney dialysis units and other medical products, develops a 4-month aggregate plan. Demand and capacity (in units) are forecast as follows: Month 1 Month 2 Month 3 Month 4 Capacity Source Labor 275 28 15 318 300 26 13 331 300 28 15 305 Regular time Overtime 225 15 Subcontract Demand 240 The cost of producingeach dialysis unit is $875 on regular time, $1,310 on overtime, and $1,600 on a subcontract. Inventory carrying cost is $100 per unit per month. There is to be no beginning or ending inventory in stock and backorders are not permitted Minimizing cost using the transportation method, the optimal cost is S(enter your response as a whole number)

Answer 1

In order to formulate the problem as a transportation model, we need to create the parameter table as below

Rows of the parameter table show supply period and columns indicate demand period

Regular cost of production in a supply period to fulfil the demand of same period is as given in the problem. For example regular production cost in period 1 to fulfil the demand of period 1 is $ 875 and overtime cost in the same supply and demand period is $ 1310. Subcontract cost is $ 1600

Regular time Cost of fulfilling demand of n period later than the current period increases by n times the carrying cost. For example, cost of fulfilling demand of period 4  (3 period later) from overtime time supply of period 1 = 1310+3*100 = 1610

While calculating net demand, opening inventory is subtracted from first month demand and required closing inventory is added to the last month demand.

Resulting parameter table is as follows

Parameter Table
Supply	Mth 1	Mth 2	Mth 3	Mth 4	Supply
Mth 1 Regular	875	975	1,075	1,175	225
Mth 1 Overtime	1,310	1,410	1,510	1,610	15
Mth 1 Subcontract	1,600	1,700	1,800	1,900	14
Mth 2 Regular		875	975	1,075	275
Mth 2 Overtime		1,310	1,410	1,510	28
Mth 2 Subcontract		1,600	1,700	1,800	15
Mth 3 Regular			875	975	300
Mth 3 Overtime			1,310	1,410	26
Mth 3 Subcontract			1,600	1,700	13
Mth 4 Regular				875	300
Mth 4 Overtime				1,310	28
Mth 4 Subcontract				1,600	15
Net Demand	240	318	331	305

Formulas:

M12 =SUM(I12:L12) copy to M12:M23

I24 =SUM(I12:I23)   copy to I24:L24

M9 =SUMPRODUCT(B12:E23,I12:L23)

The optimal cost = $ 1,091,440