Calculating capacity needed during peak period

Question

Assignment:

Question 1 : You are given the demand forecast of a product:

Period	1	2	3	4	5	6	7	8	9	10
Demand (units)	150	200	150	150	200	150	300	450	230	220

Develop a production plan using a pure level strategy if production capacity is unconstrained. Fill in the following table with the plan units and with the final inventory:

Period	1	2	3	4	5	6	7	8	9	10
Demand	150	200	150	150	200	150	300	450	230	220
Production (pure level)
Final inventory

Develop a production plan using a pure chase strategy if production capacity is unconstrained. Fill in the following table with the planned volume and with the final inventory:

Period	1	2	3	4	5	6	7	8	9	10
Demand	150	200	150	150	200	150	300	450	230	220
Production (pure chase)
Final inventory

Now, assume that the production capacity is 150 units per period during the first shift. You have the option to use overtime. The production capacity during overtime is up to 80 units per period (you use as much as you need). Moreover, you can active the second shift, if needed. The production capacity during the second shift will be 150. When a shift is activated, its capacity must be fully utilized (on/off solution).

Inventory holding cost is $2 per unit per period. Stockout cost is $15 per unit. Production cost during the first shift is $6 per unit. Production cost during the second shift is $6 per unit (loss of efficiency). Overtime cost is $8 per unit. When the production volume in one period is different from the volume of the past period, a cost of $200 is due. Answer the following questions:

The pure level plan (see your answer to question 1) is feasible given the production constraints (= you never exceed the overall production capacity, 1^st shift + 2^nd shift +overtime). Calculate the cost of the pure level plan. Fill in the table below with your numbers.

					Capacity Breakdown			Costs
Period	Demand	Production (insert a feasible plan)	Inventory	Change of production volume	1st shift	2nd shift	Overtime	1st shift	2nd shift	Overtime	Inventory	Change of production volume	Total per period
1	150
2	200
3	150
4	150
5	200
6	150
7	300
8	450
9	230
10	220

The total cost of the plan over the planning is $ .......

The pure chase plan is NOT feasible: the overall production capacity (1^st shift + 2^nd shift +overtime) is not enough in at least one period. Adjust the plan to make it feasible (the new plan will be a chase-based plan). Finally, calculate the cost of the plan. Fill in the table below with your numbers.

Hint: several different chase-based plans are possible but not all of them are feasible. The one you will choose MUST be feasible (= it MUST meet both demand and production capacity constraints)

					Capacity Breakdown			Costs
Period	Demand	Production (feasible plan)	Inventory	Change of production volume	1st shift	2nd shift	Overtime	1st shift	2nd shift	Overtime	Inventory	Change of production volume	Total per period
1	150
2	200
3	150
4	150
5	200
6	150
7	300
8	450
9	230
10	220

The total cost of the plan over the planning horizon is $ .......

Choose the best plan: .........

Question 2 :

Your production plant manufactures two products, A and B. The processing time is 2 hours per unit of Product A and 1 hour per unit of Product B. The production capacity is 350 hours per period and you can use as much as you need.

The table below shows the demand for the two products:

Month	1	2	3	4	5	6
Demand A [units]	50	20	75	35	20	25
Demand B [units]	80	160	200	150	110	50

You are asked to determine the production plan of products A and B. To keep low the costs of capacity adjustments, your manager asks you to use the pure level strategy, if feasible. If you find that the pure level strategy is not feasible, you will choose a mixed level-based plan.

Find the plan following the directions below.

Find the production rate of the Pure level plan (hint: you cannot sum up apples and oranges: you need to convert units to hours) and use that number to plan the plant production (in hours) and to calculate the final Inventory (in hours) of each period. Show your work below.

Month	1	2	3	4	5	6

The Pure Level Plan is NOT feasible. The inventory is negative in at least one period. Find a mixed level-based plan that is feasible (hint: change the production rate in periods 3 and 4). Show your plan and the inventory below.

Month	1	2	3	4	5	6
Mixed level-based plan
Final Inventory

Find the % of allocation of Production capacity of Product A and Product B. Round to the nearest whole number percent. Show your work below

% of Allocation of Product A = ...

% of Allocation of Product B = ....

Show how you found the answer:

Month	1	2	3	4	5	6

Split the mixed level-based plan between the two products using the % of allocation that you found above and find the production plans of Product A and Product B in units (hint: round down the production units because they must be whole numbers)

Month	1	2	3	4	5	6

Check if the two plans (in units) are feasible (hint: they must meet the demand of Product A and Product B). If they are not, state below what actions you need to undertake to fix the plans (hint: first try trading hours between the products; if not enough, increase the number of planned hours). Finally, show the adjusted plan (in hours), the split of the plan (in hours) between Product A and Product B, the plan (in units) of Product A and Product B, and final Inventory of Product A and Product B.

Do you need to undertake any actions to make the plan feasible? Why?

If any, state what actions you undertake to fix the plan (specify in what period):

Action 1: ......

Action 2:......

Show below the adjusted plan (in hours), the split between Product A and Product B (in hours), the plan of Product A and Product B (in units), and final Inventory of Product A and Product B (hint: inventory must be positive)

Month	1	2	3	4	5	6

Question 3 : (it's similar to Sampson Game; however, this is single-product problem)

Your company manufactures sunglasses. Demand is seasonal and has a huge peak from May to August:

Month	1	2	3	4	5	6	7	8	9	10	11	12
Demand (units)	400	500	700	900	1500	2000	2000	1500	900	700	500	400

The production capacity during the regular working time is 300 hours per month. You have the option of using overtime. The production capacity during overtime is up to 100 hours per month (you use as much as you need). If you choose to produce in a month, the capacity during regular working time must be fully utilized (on/off solution). The processing time of the product is 20 minutes per unit. You are asked to find a feasible production plan keeping the inventory level as low as possible. Follow the directions below.

Compare the demand the production capacity and figure out how many overtime periods you will need.

# overtime periods = .......

Show how you found the answer:

Now calculate the capacity needed during the peak periods (May through August) and figure out how many overtime periods you will need during the peak periods. Determine the Inventory level that must be available at the end of meet the demand during the peak periods.

# overtime periods (May through August) = .......

Target inventory at the end of April = ...

Show how you found the answer:

Check if the production capacity from January to April is enough to build up the inventory level that is needed at the end of April. How many periods of overtime do you need to use from January to April?

# overtime periods (January to April) = ....

Show how you found the answer

Finally, fill in the table with your plan, showing the Production volume in each month and the Final Inventory in each month. You must use as many overtime periods as found in the previous answers. Try to keep the inventory level as low as possible (hint 1: use as few overtime hours as possible in each overtime period; hint 2: inventory must be zero at the end of August).

Month	1	2	3	4	5	6	7	8	9	10	11	12
Demand	400	500	700	900	1500	2000	2000	1500	900	700	500	400
Production
Inventory

Provide complete and step by step solution for the question and show calculations and use formulas.